Conn. Gen. Stat. § 45a-559e: Termination of custodianship.

The custodian shall transfer in an appropriate manner the custodial property to the minor, the legal representative of the minor or the personal representative of the minor's estate upon the earlier of (1) the minor's attainment of twenty-one years of age, or (2) the minor's death, unless a prior distribution of the custodial property has been made pursuant to subsection (b) of section 45a-558k.