The custodial parent is entitled to claim the child. The custodial parent does not need a form to claim the child.
Form 8332 is used to allow the noncustodial parent to claim the child. It has to be signed by the custodial parent and filed with the noncustodial parent's tax return.
As xmasbaby said, for income tax purposes the custodial parent is determined by where the child lived, not by a court order granting custody.
