KEARSE, Circuit Judge:

This case returns to us following our remand for an evidentiary hearing and findings as to certain facts material to the petition of Stanley Ellsworth Perkins for a writ of habeas corpus. See Perkins v. Le Fevre, 642 F.2d 37 (2d Cir. 1981) ( "Perkins I"). Respondent Eugene Le Fevre, Superintendent of Clinton Correctional Facility (hereinafter the "State"), now appeals from a final judgment of the United States District Court for the Southern District of New York, Morris E. Lasker, Judge, granting Perkins's petition on the ground that the false testimony of a significant prosecution witness, and the refusal of the prosecutor to disclose a requested document that would have revealed that falsity, deprived Perkins of due process in his state trial for felony murder and other crimes. We affirm the judgment.

FACTS

Background and Perkins I

The background of Perkins's petition is set out in greater detail in Perkins I, familiarity with which is assumed. Perkins was convicted of felony murder, robbery, and grand larceny following a jury trial in which the testimony of prosecution witness Melvin Jones "`was quite important to the prosecution's case,'" and "`was probably a substantial factor in the jury's decision.'" Perkins I, 642 F.2d at 40 (quoting Recommendation of U.S. Magistrate Schreiber, dated August 23, 1978, at 13-14). As to his own prior involvements with the law, Jones testified that he had spent seventeen days in jail for parking offenses, that he had been arrested only once, that he had never been convicted of a crime, and that no charges were then pending against him.

During the trial Perkins requested that he be provided with Jones's rap sheet. The prosecutor, Joseph K. West, had a rap sheet for Jones which revealed not only the seventeen-day incarceration for parking violations, but also, in contradiction to Jones's testimony, two felony convictions and two arrests on charges that appeared to be still pending. The prosecutor refused to disclose the rap sheet to Perkins during the trial, however, on the stated ground that he thought it might be the rap sheet of a different Melvin Jones. After finally disclosing the rap sheet a month after the trial had ended, the prosecutor opposed Perkins's posttrial motions and his petition for habeas corpus on the ground that the recorded convictions and charges were not "real" but rather were window-dressing to conceal Jones's role as an undercover informer for law enforcement officials.

In Perkins I we observed that if these were real convictions, "the jury might well have assessed Jones's credibility in a different light" had it known that he had "lied on the witness stand about his past [and] had twice been found guilty of dishonest acts in the past." Id. at 41. We noted, however, that neither the state court, in denying Perkins's posttrial motions, nor the district court, in denying Perkins's habeas petition, had held an evidentiary hearing as to the genuineness of the convictions and charges disclosed on Jones's rap sheet. Hence it was undetermined whether Jones had in fact testified falsely. Accordingly, we vacated the district court's denial of the habeas petition and remanded for an evidentiary hearing on the facts with respect to (1) Jones's actual criminal record, (2) the failure of the prosecutor to make Jones's record available to the defense in time to use it at the trial, and (3) the prosecutor's knowledge as to the falsity of Jones's testimony with respect to his criminal record. Id.

The Findings on Remand

On remand a two-day hearing was held before United States Magistrate Ruth V. Washington. Documentary evidence was presented and the magistrate heard testimony from prosecutor West, two former special agents of the FBI, and two former New York City detectives. The documentary evidence showed that in addition to his parking offenses, Jones had been convicted of four crimes prior to the time of Perkins's trial. Two of those convictions were reflected on the rap sheet; and of the two not there reflected, one was reflected in a certificate of disposition available to West prior to the conclusion of the Perkins trial. The four former law enforcement agents testified to Jones's involvement with them as an informant and described certain arrests of Jones that had been designed to gain Jones's services as an informant. These witnesses were unable to testify, however, that any of the convictions shown on Jones's record related to Jones's activities as an informant. Accordingly, Magistrate Washington found that "there is no evidence that links the convictions either noted on the rap sheet or evidenced by certified copies of the dispositions with either activities of the FBI or the New York police," Report dated January 20, 1982, at 5 ("Magistrate's Report"), and concluded that

the convictions shown emerged from independent criminal behavior that was not connected with Jones's activities as an informant for law enforcement agencies. As such, the convictions were actual and not "mere window-dressing."

Id. at 6. Jones's trial testimony as to his own criminal record, therefore, was false.

Magistrate Washington found "unexplained" West's failure to provide Perkins with the record of Jones's convictions before the end of the trial. Id. at 7. Although she found it "unnecessary to characterize the subjective beliefs that the prosecutor had formed with relation either to [Jones's rap sheet] or to the accuracy of Jones's testimony," id. at 8, the magistrate found that West had had "knowledge that Jones may have testified falsely about his criminal past," id. at 7, that West had nevertheless "affirmed the accuracy of Jones's testimony . . . in answering a question from the trial court," id., and that West had "failed to correct the false statements of the witness Jones when he knew or should have known those statements were false," id. at 11. The magistrate concluded that Perkins's "conviction was obtained by the use of testimony that the prosecutor knew or had reason to know was false," id., and that the prosecutor "at petitioner's trial knowingly allowed false testimony to go uncorrected," id.

Judge Lasker, after reviewing the State's objections to the Magistrate's Report, determined that the convictions shown on Jones's rap sheet were bona fide, Memorandum Decision dated June 11, 1982, at 4, and that the prosecutor had known that Jones's rap sheet "contained material which the jury could have found to be exculpatory, because it reflected negatively on the credibility of a significant prosecution witness," id. at 5. Accordingly, Judge Lasker granted Perkins's petition for habeas corpus.

DISCUSSION

On this appeal the State contends principally that West's failure to disclose Jones's rap sheet did not constitute a violation of due process because the impeaching material went only to the collateral matter of Jones's credibility. This position has no merit.

Given the findings below, the district court correctly determined that Perkins's conviction must be set aside. Where a conviction has been obtained using "perjured testimony and ... the prosecution knew, or should have known, of the perjury," the conviction must be set aside "if there is any reasonable likelihood that the false testimony could have affected the judgment of the jury," because the use of such testimony has "involve[d] a corruption of the truth-seeking function of the trial process." United States v. Agurs, 427 U.S. 97, 103-04, 96 S.Ct. 2392, 2397, 49 L.Ed.2d 342 (1976); Annunziato v. Manson, 566 F.2d 410, 414 (2d Cir. 1977). Further, where the defendant has expressly requested that the prosecutor provide specific information and the prosecutor has refused, the conviction must be set aside if "the suppressed evidence might have affected the outcome of the trial." United States v. Agurs, supra, 427 U.S. at 104, 96 S.Ct. at 2398; Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 1196, 10 L.Ed.2d 215 (1963). In Agurs the Court stated as follows:

[I]f the subject matter of such a request is material, or indeed if a substantial basis for claiming materiality exists, it is reasonable to require the prosecutor to respond either by furnishing the information or by submitting the problem to the trial judge. When the prosecutor receives a specific and relevant request, the failure to make any response is seldom, if ever, excusable.

427 U.S. at 106, 96 S.Ct. at 2399. These principles apply both to materials going to the heart of the defendant's guilt or innocence and to materials that might well alter the jury's judgment of the credibility of a significant prosecution witness. See Giglio v. United States, 405 U.S. 150, 154, 92 S.Ct. 763, 766, 31 L.Ed.2d 104 (1972); Napue v. Illinois, 360 U.S. 264, 269, 79 S.Ct. 1173, 1177, 3 L.Ed.2d 1217 (1959).

In the present case it is undisputed that the rap sheet was specifically requested by Perkins and was withheld by the prosecutor; and we find no basis for disturbing the findings that Jones's testimony was false and that prosecutor West knew or should have known it was false. Since Jones's testimony "`was quite important to the prosecution's case,'" and "`was probably a substantial factor in the jury's decision,'" Perkins I, 642 F.2d at 40, and since "the jury might well have assessed Jones's credibility in a different light" had it known of his dishonest testimony and his past convictions for dishonest acts, id. at 41, we conclude that the prosecutor's refusal to disclose Jones's rap sheet corrupted the truth-seeking function of the trial and that the conviction of Perkins violated due process of law.

The judgment of the district court granting the writ of habeas corpus is affirmed.