*744The petitioner, Kurtis Turner, appeals following the denial of his petition for certification to appeal from the judgment of the habeas court denying his petition for a writ of habeas corpus. On appeal, the petitioner claims that the habeas court (1) abused its discretion in denying his petition for certification to *745appeal, and (2) improperly concluded that there were no violations of Brady v. Maryland , 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed. 2d 215 (1963), at his underlying criminal trial.1 For the reasons set forth herein, we agree with the petitioner and conclude that the habeas court abused its discretion in denying the petition for certification to appeal and in denying the petition for a writ of habeas corpus. Accordingly, we reverse the judgment of the habeas court and remand the matter for a new trial.
The following facts and procedural history are relevant to our resolution of this appeal. After a jury trial, the petitioner was convicted of murder in violation of General Statutes § 53a-54a(a) and sentenced to sixty years incarceration. Our prior decision on the petitioner's direct appeal in State v. Turner , 133 Conn. App. 812, 37 A.3d 183, cert. denied, 304 Conn. 929, 42 A.3d 390 (2012), set forth the following facts: "In June, 2007, the [petitioner] was living in an apartment in New London with Curtis McGill. McGill had, on several occasions, sold the drug PCP to Lakisha Alexander, the sister of Vernall Marshall, the victim. At some point during or near in time to April, 2007, Alexander stole some PCP from McGill's apartment. McGill later discovered that she had done so and told her that she owed him a favor.
"On June 19, 2007, Alexander, the victim, and two of the victim's friends encountered McGill, who was alone, on Bank Street in New London. The victim approached McGill, and the two of them conversed *1167apart from the others. During the conversation, the victim told McGill that he would not let McGill disrespect his sister. After *746talking with McGill for two to five minutes, the victim walked back to Alexander and the others. McGill appeared to be upset, remarking several times that he felt threatened.
"Subsequent to this encounter with the victim, McGill made a telephone call, and, three to five minutes later, a car came down Bank Street and parked next to McGill. Three individuals got out of the car, one of whom was the [petitioner], who was holding a gun. The [petitioner] waved the gun in the air and pointed it at the victim, proclaiming, 'I'll do anybody out here,' 'You want to die?' and, 'somebody is going to die.' After approximately one minute, McGill told the [petitioner] to stop, and the [petitioner] lowered the gun and returned to the car with the other two individuals. The three of them left in the car, and McGill walked away from the victim, Alexander and the others. On the way back to the apartment, the [petitioner] repeatedly remarked that '[w]ithin forty-eight hours somebody is going to die.'
"On the night of June 20, 2007, the victim was in New London having drinks with friends. He had gone into New London with his friend, Shannon Johnson, and later that evening he met up with Alexander. In the early morning hours of June 21, 2007, the victim again met up with Johnson on the sidewalk just outside the front entrance to Ernie's Café on Bank Street. At this time, the [state claims, the petitioner] approached the victim and shot him in the head. Emergency personnel took the victim by ambulance to a nearby hospital, where, after approximately twelve minutes of medical care, he was pronounced dead.
"On January 8, 2008, the state filed an information charging the [petitioner] with murder in violation of § 53a-54a(a). On May 28, 2008, attorney Raul [Davila-Carlos] was appointed as a special public defender to *747represent the [petitioner], which he did for approximately one year without complaint. Beginning on the first day of jury selection on May 28, 2009, the [petitioner] made several requests that the court remove [Davila-Carlos] as his counsel and either appoint new counsel or allow him to represent himself. The court denied the [petitioner's] requests to have new counsel appointed, noting that the requests were made on the eve of trial. The trial then proceeded with [Davila-Carlos] representing the [petitioner] ....
"On July 16, 2009, at the conclusion of the state's case-in-chief, the [petitioner] made an oral motion for a judgment of acquittal, asserting that the evidence was insufficient to establish guilt beyond a reasonable doubt, which the court denied. The jury returned a verdict of guilty, and the [petitioner] was sentenced to sixty years incarceration." Id., at 814-16, 37 A.3d 183. This court affirmed the petitioner's conviction on direct appeal. See id., at 814, 37 A.3d 183.
On March 1, 2013, the petitioner, in a self-represented capacity, filed a petition for writ of habeas corpus. On May 8, 2015, the petitioner, represented by appointed counsel, filed the amended petition operative in this appeal. In the amended petition, the petitioner alleged that (1) his constitutional right to the effective assistance of trial counsel was violated, (2) his right to due process was violated by the prosecuting authority's knowing presentation of false testimony, and (3) his right to due process was violated by the prosecuting authority's failure to disclose material *1168exculpatory evidence.2 The habeas trial was held over three days from September 28, 2015 to September 30, 2015. The petitioner presented the testimony of, inter alia, Raul Davila-Carlos, the petitioner's trial counsel, and John P. *748Gravelec-Pannone, the prosecuting attorney in the petitioner's case. Following the trial, the habeas court, Sferrazza, J. , denied the petition in a written decision in which it concluded that the petitioner had not met his burden to prove ineffective assistance of counsel or a violation of his due process rights. Thereafter, the habeas court denied the petition for certification to appeal, and this appeal followed. Additional facts and procedural history will be set forth as necessary.
I
The petitioner claims that the habeas court abused its discretion in denying his petition for certification to appeal from the denial of his petition for a writ of habeas corpus with respect to his claim of due process violations. We agree.
"Faced with a habeas court's denial of a petition for certification to appeal, a petitioner can obtain appellate review of the dismissal of his petition for habeas corpus only by satisfying the two-pronged test enunciated by our Supreme Court in Simms v. Warden , 229 Conn. 178, 640 A.2d 601 (1994), and adopted in Simms v. Warden , 230 Conn. 608, 612, 646 A.2d 126 (1994). First, [the petitioner] must demonstrate that the denial of his petition for certification constituted an abuse of discretion .... Second, if the petitioner can show an abuse of discretion, he must then prove that the decision of the habeas court should be reversed on the merits .... To prove that the denial of his petition for certification to appeal constituted an abuse of discretion, the petitioner must demonstrate that the [resolution of the underlying claim involves issues that] are debatable among jurists of reason; that a court could resolve the issues [in a different manner]; or that the questions are adequate to deserve encouragement to proceed further ....
*749"In determining whether the habeas court abused its discretion in denying the petitioner's request for certification, we necessarily must consider the merits of the petitioner's underlying claims to determine whether the habeas court reasonably determined that the petitioner's appeal was frivolous. In other words, we review the petitioner's substantive claims for the purpose of ascertaining whether those claims satisfy one or more of the three criteria ... adopted by [our Supreme Court] for determining the propriety of the habeas court's denial of the petition for certification." (Citations omitted; internal quotation marks omitted.) Sanders v. Commissioner of Correction , 169 Conn. App. 813, 821-22, 153 A.3d 8 (2016), cert. denied, 325 Conn. 904, 156 A.3d 536 (2017).
As discussed in part II of this opinion, because the resolution of the petitioner's underlying claim involves issues that are debatable among jurists of reason and could have been resolved by a court in a different manner, we conclude that the habeas court abused its discretion in denying certification to appeal from the denial of the petition for a writ of habeas corpus.
II
The petitioner claims that his due process rights were violated by the prosecuting *1169attorney's knowing presentation of false or misleading testimony and failure to disclose material impeachment evidence as required by Brady v. Maryland , supra, 373 U.S. at 83, 83 S.Ct. 1194. Specifically, the petitioner argues that (1) Gravelec-Pannone failed to correct the false testimony of Alice Philips, a cooperating witness for the prosecution, that she had not received consideration in exchange for her testimony; and (2) the prosecution failed to disclose the material exculpatory evidence that the state had provided consideration in exchange for the testimony of Philips, who was a friend of the victim and testified on behalf of the *750state about the dispute among the petitioner, McGill and the victim.
The following additional facts are relevant to this issue. In her initial statement to the police, Philips told them that McGill was the individual who said that somebody was going to be dead within forty-eight hours. Prior to testifying at the petitioner's trial, Gravelec-Pannone told Philips that if he believed she testified truthfully, he would notify the prosecutor handling her own pending charges of her cooperation. The State's Attorney's Office also purchased plane fare for Philips, who traveled from Michigan to Connecticut to testify at the petitioner's trial.
At the petitioner's trial, Philips admitted that she was flown in by the state to answer to her outstanding warrants and had just been arraigned on those charges. Her defense counsel was present throughout her testimony. Notably, Philips changed her story when she testified at trial that the petitioner, rather than McGill, uttered the statement that somebody was going to die within forty-eight hours. Furthermore, when asked if she was hoping for any consideration, aside from the plane fare, in exchange for her testimony, Philips answered, "no." Gravelec-Pannone did not correct that statement.
After testifying at the petitioner's trial, Philips was transported to the geographical area number ten courthouse in New London to plead guilty on her outstanding charges. Peter A. McShane, a prosecutor in that courthouse at the time Philips was put to plea, informed the court, McMahon, J. , that she had cooperated and testified on behalf of the state at the petitioner's trial. Thereafter, Philips received a one year sentence, fully suspended, with a one year conditional discharge where the sole condition was not to return to Connecticut. At the petitioner's habeas trial, McShane testified that Philips' case "just showed up on the docket," and that *751he did not remember who advised him of the fact that Philips had testified in a case in the part A court. Additionally, McShane testified that it did not appear that he or anyone else working in his office at the geographical area number ten courthouse ever made a sentencing recommendation to Judge McMahon; it appeared that the judge sua sponte came up with a court-indicated sentence for Philips.
Gravelec-Pannone testified that after Philips was done testifying in the petitioner's case, he instructed his inspector to let the prosecutor in Philips' case know that she had testified to his satisfaction. Gravelec-Pannone acknowledged that notifying the prosecutor in Philips' case that she had testified helpfully was a form of consideration in exchange for her testimony, "but no specific consideration that you're going to get this deal up front if you do that." He indicated, however, that he did not correct Philips' statement that she was not expecting consideration because he did not want to impeach his own witness. He indicated that his office would not have told the prosecutors in the geographical area number ten courthouse what to do with Philips'
*1170cases, but would make them aware that she was going to be a witness in their case and would keep them posted as to what happened in the part A court. He also testified that Philips' father was a marshal in the New London part A court, and that he had "used his efforts" to persuade Philips to come back from Michigan to "testify and face the music" regarding her pending charges in Connecticut. After Philips' outstanding cases were resolved, Gravelec-Pannone "communicated [to Davila-Carlos] [the] fact that [Philips'] cases were resolved, and she would be heading back to Michigan shortly thereafter, but [Davila-Carlos] was aware that [Philips] was still in New London and capable of being served with a subpoena if [Davila-Carlos] needed to do that." The State's Attorney's Office paid for an *752airline ticket for Philips to return to Michigan the day after she pleaded guilty.
Davila-Carlos testified that he did not have a recollection of the state informing him of the agreement with Philips, but that he could have argued the issue of Philips' credibility to the jury if he had known of a prior agreement. He also testified that he had not wanted to discredit Philips' testimony too much because he believed her recollection of the dispute between the petitioner and the victim aided in his self-defense argument.
On the basis of this testimony, the habeas court concluded that the petitioner had failed to establish a Brady violation because "no exculpatory evidence was withheld from the petitioner, nor did [Philips] testify falsely at his criminal trial."
We next set forth our standard of review and the applicable legal principles governing Brady claims. As set forth by the United States Supreme Court in Brady v. Maryland , supra, 373 U.S. at 87, 83 S.Ct. 1194, "[t]o establish a Brady violation, the [petitioner] must show that (1) the government suppressed evidence, (2) the suppressed evidence was favorable to the [petitioner], and (3) it was material [either to guilt or to punishment]." (Internal quotation marks omitted.) Morant v. Commissioner of Correction , 117 Conn. App. 279, 295, 979 A.2d 507, cert. denied, 294 Conn. 906, 982 A.2d 1080 (2009). "Whether the petitioner was deprived of his due process rights due to a Brady violation is a question of law, to which we grant plenary review." (Internal quotation marks omitted.) Peeler v. Commissioner of Correction , 170 Conn. App. 654, 689, 155 A.3d 772, cert. denied, 325 Conn. 901, 157 A.3d 1146 (2017).
"[T]he suppression by the prosecution of evidence favorable to an accused upon request violates due process [when] the evidence is material either to guilt or *753to punishment, irrespective of the good faith or bad faith of the [prosecutor] .... The United States Supreme Court also has recognized that [t]he jury's estimate of the truthfulness and reliability of a ... witness may well be determinative of guilt or innocence, and it is upon such subtle factors as the possible interest of the witness in testifying falsely that a defendant's life or liberty may depend. Napue v. Illinois , 360 U.S. 264, 269, 79 S.Ct. 1173, 3 L.Ed. 2d 1217 (1959). Accordingly, the Brady rule applies not just to exculpatory evidence, but also to impeachment evidence ... which, broadly defined, is evidence having the potential to alter the jury's assessment of the credibility of a significant prosecution witness .... Because a plea agreement is likely to bear on the motivation of a witness who has agreed to testify for the state, such agreements are potential impeachment evidence that the state must disclose ....
"[A] prosecutor's failure to disclose favorable evidence will constitute a *1171violation of Brady only if the evidence is found to be material .... In a classic Brady case ... the evidence will be deemed material only if there would be a reasonable probability of a different result if the evidence had been disclosed." (Internal quotation marks omitted.) State v. Jordan , 314 Conn. 354, 370, 102 A.3d 1 (2014).
A
We first address the petitioner's claim that the prosecutor's failure to correct Philips' false testimony that she did not expect any consideration for her testimony deprived him of his due process right to a fair trial under Brady . In response, the respondent, the Commissioner of Correction, argues that even if the witness did testify falsely and the prosecutor failed to correct that testimony, there was no reasonable likelihood that *754the misleading testimony could have affected the judgment of the jury. We agree with the petitioner.
We set forth the legal principles applicable to this issue. The state has a duty to correct the record if it knows that a witness has testified falsely. See Diaz v. Commissioner of Correction , 174 Conn. App. 776, 796, 166 A.3d 815 ("[D]ue process is ... offended if the state, although not soliciting false evidence, allows it to go uncorrected when it appears .... If a government witness falsely denies having struck a bargain with the state, or substantially mischaracterizes the nature of the inducement, the state is obliged to correct the misconception." [Internal quotation marks omitted.] ), cert. denied, 327 Conn. 957, 172 A.3d 204 (2017) ; see also Gomez v. Commissioner of Correction , 178 Conn. App. 519, 539, 176 A.3d 559 (2017) ("[r]egardless of the lack of intent to lie on the part of the witness, Giglio [v. United States , 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed. 2d 104 (1972) ] and Napue [v. Illinois , supra, 360 U.S. at 264, 79 S.Ct. 1173 ] require that the prosecutor apprise the court when he knows that his witness is giving testimony that is substantially misleading" [internal quotation marks omitted] ), cert. granted on other grounds, 328 Conn. 916, 180 A.3d 962 (2018).3
"When ... a prosecutor obtains a conviction with evidence that he or she knows or should know to be *755false, the materiality standard [of Brady ] is significantly more favorable to the defendant. [A] conviction obtained by the knowing use of perjured testimony is fundamentally unfair, and must be set aside if there is any reasonable likelihood that the false testimony could have affected the judgment of the jury .... This standard ... applies whether the state solicited the false testimony or allowed it to go uncorrected ... and is not substantively different from the test that permits the state to avoid having a conviction set aside, notwithstanding a violation of constitutional magnitude, upon a showing that the violation was harmless beyond a reasonable doubt .... This strict *1172standard of materiality is appropriate in such cases not just because they involve prosecutorial misconduct, but more importantly because they involve a corruption of the truth-seeking function of the trial process .... In light of this corrupting effect, and because the state's use of false testimony is fundamentally unfair, prejudice sufficient to satisfy the materiality standard is readily shown ... such that reversal is virtually automatic ... unless the state's case is so overwhelming that there is no reasonable likelihood that the false testimony could have affected the judgment of the jury ....
"In accordance with these principles, our determination of whether [the witness'] false testimony was material under Brady and its progeny requires a careful review of that testimony and its probable effect on the jury, weighed against the strength of the state's case and the extent to which [the petitioner was] otherwise able to impeach [the witness]." (Emphasis in original; internal quotation marks omitted.) State v. Jordan , supra, 314 Conn. at 370-71, 102 A.3d 1.
Applying the foregoing principles to the petitioner's claim, we conclude that the prosecutor's failure to correct the false testimony of Philips that she was not *756hoping for any consideration in exchange for her testimony violated the petitioner's due process right to a fair trial. Weighing the probable effect of Philips' testimony against the petitioner's ability to impeach her and the weaknesses of the state's case, we conclude that there is a reasonable likelihood that the false testimony could have affected the judgment of the jury. The state's theory of the case, namely, that the petitioner shot the victim as part of the dispute between McGill, the petitioner and the victim, was largely dependent on Philips' testimony. Philips testified that on the day before the shooting, she witnessed the petitioner pull a gun out of his hoodie with his right hand, wave the gun around, and point it at the victim. She testified that the petitioner said, "you want to die, you want to die," followed by, "before [forty-eight] hours they was gonna die." The petitioner put the gun back into his hoodie when McGill told him to stop. The petitioner and Philips then left the scene in the car of a friend, Shauntay. On the ride back to Shauntay's house, the petitioner again stated, "within [forty-eight] hours somebody is going to die."
Alexander was the only other witness who testified about the dispute between the petitioner and the victim on the night before the shooting, but her testimony was far less detailed than Philips' description of the event. Alexander testified that the petitioner had a gun and "kind of waved it in the air," and stated, "I'll do anybody out here." Alexander, however, had substantial credibility issues; she was the sister of the victim, had a significant PCP addiction during 2007, and admitted that she was the individual who stole PCP from McGill in the months before the shooting. Although Alexander claimed not to know the substance of the argument between the victim, the petitioner and McGill, Philips testified that the three were clearly arguing about Alexander owing McGill money for the PCP she stole. Additionally, Philips testified that Alexander appeared to be high on PCP at the time of the dispute.
*757The state also offered a surveillance video into evidence to support its theory that the petitioner had killed the victim. On the night of June 20, 2007, Ernie's Café had surveillance cameras pointed in the direction of the entrance to the bar. At approximately 12:19 a.m. on June 21, 2007, the video recording showed the petitioner get up from a table where he was sitting with friends and walk toward the entrance to the bar. The petitioner was dressed in a *1173dark shirt, light colored jeans, and a black baseball cap. The petitioner reached into the waistband of his jeans with his right hand as he walked to the front door. As the petitioner reached the entrance, the video recording showed the victim fall to the ground just outside the front door. The petitioner then ran out the front door and to his right toward Golden Street.
The state acknowledged, however, that the video does not clearly show the petitioner as the shooter of the victim.4 The state was also unable to offer any physical evidence that identified the petitioner as the shooter of the victim, such as fingerprints, DNA, or bullet fragments. Because the state relied heavily on Philips' testimony in its closing argument, labelling her a "very important" witness in the case who "straddle[d] or reflect[ed] both sides in this matter," her credibility was important to the jury's verdict. The petitioner's trial counsel was unable to cross-examine or impeach Philips regarding her false testimony about the consideration she anticipated receiving for her favorable testimony because he was not informed that Philips received any consideration for such testimony until after she was done testifying at the petitioner's trial.
Against this background, we conclude that the prosecutor's failure to correct Philips' false testimony was *758material for the purposes of Brady . Philips was a crucial witness for the state. Her testimony provided evidence of motive, intent, and means on the part of the petitioner. Further, her testimony negated any possible effect that the self-defense argument by the petitioner's trial counsel may have had on the jury because it painted the petitioner as an aggressor. Therefore, any evidence that would affect her credibility would be vital to the defense. The petitioner is entitled to a new trial because the strength of the state's case was not so overwhelming that there is no reasonable likelihood that the witness' false testimony affected the judgment of the jury. Cf. State v. Jordan , supra, 314 Conn. at 372, 102 A.3d 1.
B
The petitioner also claims that he suffered a violation of his due process rights under Brady because the prosecution did not disclose Philips' informal agreement with the state to receive consideration in exchange for her testimony at the petitioner's trial. In response, the respondent argues that no material evidence was withheld from the petitioner because Philips' pending charges were disclosed. Because we determine that the habeas court applied an incorrect legal standard to this issue, the petitioner is entitled to a new trial.
The habeas court's conclusion that "no exculpatory evidence was withheld from the petitioner" was premised on its factual finding that there was no evidence of a plea agreement between the state and Philips. Our case law is clear, however, that the petitioner need not establish the existence of a formal plea agreement in order to prove a Brady violation. "[E]vidence that merely suggests an informal understanding between the state and a state's witness may constitute impeachment evidence for the purposes of Brady .... Such evidence is by no means limited to the existence of plea agreements." (Citation omitted; emphasis in original.)
*759*1174Diaz v. Commissioner of Correction , supra, 174 Conn. App. at 798, 166 A.3d 815. "An agreement by a prosecutor with a cooperating witness to bring the witness' cooperation to the attention of the judge who later sentences the witness on his own pending criminal charges is a deal that must be disclosed to the defendant against whom [she] testifies, even if the deal does not involve a specific recommendation by the prosecutor for the imposition of a particular sentence." Hines v. Commissioner of Correction , 164 Conn. App. 712, 725, 138 A.3d 430 (2016) ; see also Walker v. Commissioner of Correction , 103 Conn. App. 485, 493, 930 A.2d 65 ("[a]ny such understanding or agreement between any state's witness and the state police or the state's attorney clearly falls within the ambit of the Brady principles"), cert. denied, 284 Conn. 940, 937 A.2d 698 (2007).
It is generally undisputed that there was an informal agreement between Philips and the prosecutor for her cooperation at the petitioner's trial, and that she received consideration for her favorable testimony. Gravelec-Pannone acknowledged that notifying the prosecutor in Philips' case that she had cooperated at the petitioner's trial was a form of consideration. The court, therefore, applied the incorrect legal standard when it determined that the petitioner had not proven a Brady violation because there was no evidence of a formal plea agreement between Philips and the state.
"[W]hether the court applied the correct legal standard is a question of law subject to plenary review .... When an incorrect legal standard is applied, the appropriate remedy is to reverse the judgment of the trial court and to remand the matter for further proceedings." (Internal quotation marks omitted.) Carraway v. Commissioner of Correction , 144 Conn. App. 461, 471, 72 A.3d 426 (2013), appeal dismissed, 317 Conn. 594, 119 A.3d 1153 (2015). Accordingly, the petitioner is entitled to a new trial on this basis.
*760In sum, we conclude that the petitioner has established that he suffered a Brady violation at his criminal trial when the prosecutor failed to correct Philips' false testimony that she did not expect to receive any consideration, aside from plane fare, in exchange for her testimony. Additionally, we conclude that the habeas court applied an incorrect legal standard in determining whether the petitioner suffered a Brady violation in that Philips' informal agreement with the state was not disclosed to the defense. On those bases, we further conclude that the habeas court abused its discretion in denying the petition for certification to appeal from the denial of the petition for a writ of habeas corpus.
The judgment is reversed and the case is remanded with direction to render judgment granting the petition for a writ of habeas corpus, to vacate the petitioner's conviction under § 53a-54a(a) and to order a new trial on that offense.
In this opinion the other judges concurred.