Conn. Gen. Stat. § 46b-387: Recognition of order modified in another state.

If a child support order issued by a tribunal of this state is modified by a tribunal of another state which assumed jurisdiction pursuant to the Uniform Interstate Family Support Act, a tribunal of this state (1) may enforce its order that was modified only as to arrears and interest accruing before the modification; (2) may provide appropriate relief for violations of its order which occurred before the effective date of the modification; and (3) shall recognize the modifying order of the other state, upon registration, for the purpose of enforcement.