A state court judge cannot order the IRS to do anything. However, a state court judge could order the custodial parent to sign form 8332 releasing the child tax credit and the dependent exemption to the noncustodial parent as part of a child support agreement or divorce settlement. (The custodial parent always keeps the right to claim the child as a qualifying person for head of household status and the earned income credit. That cannot be transferred under any circumstances.)
The dependent exemption is often awarded to the noncustodial parent in alternating years in divorce cases. Whether this is acceptable to you or not is something you need to discuss with your attorney.
Note that if you refuse to sign the form, the other parent cannot claim anything with the IRS. The IRS does not respect state court orders, only the signed form. However, if you do not sign the form, your ex can take you back to court and file a contempt charge for violating the court order.
