Depending on state laws regarding community property, the IRS may intercept all or part of your or your spouse's share of the federal tax refund to pay your support debt.
If you and your new spouse (called a non-obligated or "injured" spouse) file a joint income tax return, your spouse may be able to get back his or her share of the refund. To claim their portion of any refund due, your spouse may file an Injured Spouse Allocation of a Joint Return (Form 8379) with the IRS. The IRS encourages an injured spouse to file the claim at the same time the tax return is filed.
Check with your child support agency for more information.