Conn. Gen. Stat. § 46b-224: Effect of court order changing or transferring guardianship or custody of child on preexisting support order.

Whenever the Probate Court, in a guardianship matter under chapter 802h, or the Superior Court, in a family relations matter, as defined in section 46b-1, orders a change or transfer of the guardianship or custody of a child who is the subject of a preexisting support order, and the court makes no finding with respect to such support order, such guardianship or custody order shall operate to: (1) Suspend the support order if guardianship or custody is transferred to the obligor under the support order; or (2) modify the payee of the support order to be the person or entity awarded guardianship or custody of the child by the court, if such person or entity is other than the obligor under the support order.