Conn. Gen. Stat. § 46b-116b: Jurisdiction over Indian child custody matters.

An Indian tribe shall have exclusive jurisdiction as to any state court over any child custody proceeding involving an Indian child who resides or is domiciled within the reservation of such tribe, except where such jurisdiction is otherwise vested in the state by existing federal law. Where an Indian child is a ward of a tribal court, the tribal court shall retain exclusive jurisdiction, notwithstanding the residence or domicile of the child.