First, let me say that every state is different so you must check with the particular state and many will not provide specific information but they have procedures that must be followed.  Usually with an income tax offset, the money taken is not automatically given to the ex spouse for the child support, there is a waiting period so claims- like Injured Spouse- can be processed.  For child support, they will not make the ex-wife "pay back" the money just because you qualify to get the refund.