You can't do that (what the judge decreed in the divorce agreement). It's in conflict with tax law. The Child Tax goes together with the Dependency. Whichever parent claims the dependency also claims the child tax credit.
There is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/exemption/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status (unless filing jointly with new spouse), and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner.
Note that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has released the dependency to him.
"Custodial parent" is determined by physical custody, not legal custody.
