Child support does interact with other aspects of taxes. For example, a portion of alimony can be considered as child support payments, and thus not tax deductible for the person paying the alimony.
Also, federal tax refunds can be confiscated and used to pay past-due child support. The Financial Management Service (a division of the US Treasury Department that processes tax refunds) will use a person's refund money and forward it to the state or local agency to pay off child support, student loans, and state taxes in arrears. (Source: Treasury Offset Program.)