Conn. Gen. Stat. § 45a-606: (Formerly Sec. 45-43). Father and mother joint guardians.

The father and mother of every minor child are joint guardians of the person of the minor, and the powers, rights and duties of the father and the mother in regard to the minor shall be equal. If either father or mother dies or is removed as guardian, the other parent of the minor child shall become the sole guardian of the person of the minor.