Conn. Gen. Stat. § 52-172: Declarations and memoranda of deceased persons.

In actions by or against the representatives of deceased persons, and by or against the beneficiaries of any life or accident insurance policy insuring a person who is deceased at the time of the trial, the entries, memoranda and declarations of the deceased, relevant to the matter in issue, may be received as evidence. In actions by or against the representatives of deceased persons, in which any trustee or receiver is an adverse party, the testimony of the deceased, relevant to the matter in issue, given at his examination, upon the application of such trustee or receiver, shall be received in evidence.