REVISED SUMMARY ORDER

Petitioner-appellant Damian Rossney (“Rossney”) appeals from an order of the United States District Court for the Southern District of New York (Koeltl, J.), denying his petition for a writ of habeas corpus. Rossney is serving a sentence of eight and one-third to twenty-five years for conspiracy in the second degree, concurrently with a sentence of five to fifteen years for criminal facilitation, in connection with four 1986 murders. In January 1997, Rossney appeared before the New York State Parole Board (“the Board") for a parole hearing. The Board ultimately denied parole on the ground that Rossney’s “responses at [the] hearing demonstrate[d][his] lack of insight” into his criminal conduct. Rossney instituted an Article 78 proceeding in the New York Supreme Court, challenging the Board’s decision on the grounds that the Board’s questions of him at the parole hearing violated his Fifth Amendment rights. Rossney appealed the Supreme Court’s dismissal of his Article 78 petition to the Appellate Division, which affirmed the Supreme Court’s dismissal. Rossney v. N.Y. State Bd. of Parole, 267 A.D.2d 648, 699 N.Y.S.2d 319 (App.Div.3d Dep’t 1999). The New York Court of Appeals denied Rossney leave to appeal the Appellate Division’s decision. Rossney v. New York State Bd. of Parole, 94 N.Y.2d 759, 705 N.Y.S.2d 6, 726 N.E.2d 483 (2000). Rossney then filed the instant petition for a writ for habeas corpus, claiming, inter alia, that the Board violated his Fifth Amendment rights by relying on his failure to volunteer information to police investigators and his failure to testify at his co-defendant’s trial in denying parole. The district court dismissed his petition on the merits. Rossney v. Travis, 2003 WL 135692, at *8 (S.D.N.Y. Jan.17, 2003). *287Nevertheless, finding Rossney’s Fifth Amendment claim “adequate to receive further review,” id. at *13, the district court granted Rossney a certificate of appealability on that claim.1

The Antiterrorism and Effective Death Penalty Act of 1996 (“AEDPA”) requires us to defer to a state court’s adjudication of the merits of a claim. See 28 U.S.C. § 2254(d). Rossney argues that because the Appellate Division made only a “single sentence reference” to his Fifth Amendment claim, its decision does not constitute an adjudication on the merits for purposes of determining the applicable standard of review. We have held that a state court “adjudicates” a petitioner’s federal constitutional claims “on the merits” when it states that it is disposing of the claims on the merits and reduces its disposition to judgment. Cotto v. Herbert, 331 F.3d 217, 230 (2d Cir. 2003). Although the Appellate Division did not provide an elaborate explanation for its decision, there is no indication that its decision was disposed of on procedural grounds rather than on the merits, or that it misconstrued Rossney’s claim. Moreover, a state claim may be “adjudicated on the merits,” and thus entitled to deferential review, “even if the state court does not explicitly refer to ... relevant federal case law.” Sellan v. Kuhlman, 261 F.3d 303, 311-12 (2d Cir. 2001). Because the Appellate Division’s decision here constituted an adjudication on the merits, it is entitled to deferential review and may not be overturned absent a showing that it “involved an unreasonable application of [] clearly established federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d)(1).

Rossney argues that he is entitled to a writ of habeas corpus because the Board impermissibly penalized him, in violation of his Fifth Amendment rights, for his failure to volunteer information when he was first approached by the police or testify against his codefendant. Although the Fifth Amendment’s privilege against compelled self-incrimination in a criminal prosecution also protects against being compelled to provide information that may be used in future criminal proceedings, Baxter v. Palmigiano, 425 U.S. 308, 316-18, 96 S.Ct. 1551, 47 L.Ed.2d 810 (1976), there is no indication that Rossney invoked his Fifth Amendment privilege during the criminal investigation or at the parole hearing. See Roberts v. United States, 445 U.S. 552, 559, 100 S.Ct. 1358, 63 L.Ed.2d 622 (1980) (“The Fifth Amendment privilege against compelled self-incrimination is not self-executing.”). Even assuming, without concluding, that Rossney did invoke his Fifth Amendment rights in refusing to volunteer information to the police or testify against his co-defendant, there is no indication that the Board’s questions were intended to penalize Rossney for so doing. Under New York law, in determining whether parole is appropriate, the Board must consider whether the inmate “will live and remain at liberty without violating the law, and that his release is not incompatible with the welfare of society and will not so *288deprecate the seriousness of his crime as to undermine respect for the law.” N.Y. Exec. Law § 259-i(2)(c)(A). In context, it is clear that in questioning Rossney, the Board was simply ensuring that Rossney understood the gravity of the offenses for which he was convicted. We agree with the district court and therefore conclude that in making the decision to deny Rossney parole, the Board properly considered the fact that Rossney’s “responses at [the parole] hearing demonstrate[d][his] lack of insight” into the gravity of his offenses, and determined that granting parole “would deprecate the gravity of [Rossney’s] crime and ... would undermine respect for the law.”

Further, we reject Rossney’s claim that in denying his Fifth Amendment claim, the district court misconstrued the facts of the case, incorrectly identified controlling law, and misapplied Supreme Court precedent. Finally, although the Board and the reviewing courts misstated minor factual issues, we reject Rossney’s contention that these misstatements were material to the ultimate disposition of the proceedings.

For the foregoing reasons, the judgment of the District Court is AFFIRMED.