
949 A.2d 554 (2008)
108 Conn.App. 768
Ronnie HOLLEY
v.
COMMISSIONER OF CORRECTION.
No. 28522.
Appellate Court of Connecticut.
Argued May 1, 2008.
Decided July 1, 2008.
*555 Gennaro Bizzarro, special public defender, for the appellant (petitioner).
Timothy F. Costello, deputy assistant state's attorney, with whom, on the brief, were Michael Dearington, state's attorney, and Linda N. Howe, senior assistant state's attorney, for the appellee (respondent).
BISHOP, GRUENDEL and BEACH, Js.
PER CURIAM.
The petitioner, Ronnie Holley, appeals following the denial of certification to appeal from the judgment of the habeas court denying his petition for a writ of habeas corpus. The petitioner claims that the court abused its discretion in denying certification to appeal and improperly rejected his claim that his trial counsel provided ineffective assistance. He also claims that the habeas court made an improper evidentiary ruling that prevented him from proving his claim. We dismiss the petitioner's appeal.
The petitioner claimed, in his habeas trial, that his trial counsel rendered ineffective assistance because he failed (1) to conduct an adequate investigation into the victim's prior course of conduct, (2) to impeach the victim's testimony and (3) to inform the petitioner of the kidnapping charge against him. The court concluded that the petitioner failed to satisfy his burden under Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), in that he did not establish by a preponderance of the evidence that counsel's performance was deficient and that the deficient performance prejudiced the defense for any of these claims.
"The standard of review for a habeas court's denial of a petition for certification to appeal requires the petitioner to prove that the denial of the petition for certification was an abuse of discretion and also that the decision of the habeas court should be reversed on the merits." Key v. Commissioner of Correction, 106 Conn.App. 211, 212, 942 A.2d 417, cert. denied, 287 Conn. 904, 947 A.2d 342 (2008). To prove 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." (Internal quotation marks omitted.) Simms v. Warden, 230 Conn. 608, 616, 646 A.2d 126 (1994).
The following facts and procedural history are relevant to our review of the petitioner's appeal. Following a five day trial, the jury found the petitioner guilty of the crimes of sexual assault in the first degree *556 in violation of General Statutes § 53a-70 and assault in the third degree in violation of General Statutes § 53a-61(a)(1). The jury found the petitioner not guilty of kidnapping in the first degree in violation of General Statutes § 53a-92(a)(2)(A). The trial court imposed a total effective sentence of fifteen years imprisonment, suspended after ten years, and ten years probation. The petitioner's amended petition for a writ of habeas corpus was filed on April 15, 2005, alleging that his trial counsel was ineffective for not having adequately investigated the victim's prior course of conduct, for not having adequately impeached the victim's testimony and for not informing the petitioner of the kidnapping charge against him. The habeas court found that the petitioner's trial counsel sufficiently investigated the victim's prior course of conduct and that the petitioner failed to provide evidence in support of his claim that counsel did not adequately impeach the victim. Additionally, the court credited testimony that the petitioner was informed of the kidnapping charge against him despite his contrary testimony. The court denied the subsequent petition for certification to appeal, and this appeal followed.
After a careful review of the record and briefs, we agree with the court that the petitioner failed to satisfy his burden of proving that counsel's performance was deficient. The court's determination that the petitioner's trial counsel was not ineffective was a purely factual determination. "[T]he habeas court, as the trier of facts, is the sole arbiter of the credibility of witnesses and the weight to be given to their testimony." (Internal quotation marks omitted.) Vazquez v. Commissioner of Correction, 107 Conn. App. 181, 187, 944 A.2d 429 (2008). Therefore, we defer to the court's findings.[1]
The petitioner also claims on appeal that the habeas court should have admitted records from Catholic Relief Services because those records would have revealed that the victim received or believed that she received rental assistance contingent on her filing domestic abuse complaints. We are unpersuaded. As asserted at trial, this claim was no more than a theory without any evidentiary basis.[2] Additionally, the regional coordinator for Catholic Relief Services' "Welfare-to-Work" program testified that although the victim did receive rental assistance from her organization, the assistance was not initiated because of, and was never contingent on, the victim's filing a domestic violence complaint. As there was no other testimony indicating a link between rental assistance and domestic violence claims, the court did not abuse its discretion by refusing to admit the records. Furthermore, even if the exclusion of the records *557 was improper, any error was harmless because the regional coordinator testified that the records made no mention of domestic violence complaints, and she was available for cross-examination. Because there are no issues that are debatable among reasonable jurists, that a court could resolve differently or that deserve further proceedings, we conclude that the court did not abuse its discretion in denying the petition for certification to appeal.
The appeal is dismissed.
NOTES
[1]  To the extent that the habeas court failed to address the petitioner's claim that his trial counsel was ineffective in impeaching the victim's testimony, the failure of the petitioner to request an articulation renders the record inadequate for review. When "the court's memorandum of decision is devoid of any findings or analysis on the issue, and . . . the petitioner [does] not seek an articulation, the record is inadequate and we cannot review [the petitioner's] claim." Bowden v. Commissioner of Correction, 93 Conn.App. 333, 342, 888 A.2d 1131, cert. denied, 277 Conn. 924, 895 A.2d 796 (2006).
[2]  At the time of the assaults, the victim was the petitioner's girlfriend, and the assaults took place in the residence that they shared. State v. Holley, 90 Conn.App. 350, 352, 877 A.2d 872, cert. denied, 275 Conn. 929, 883 A.2d 1249 (2005). Therefore, the petitioner's claim that the victim believed, or that the rental assistance actually was, contingent on the victim's filing domestic violence complaints appears to be directed at undermining the credibility of the victim's testimony.
