There is a conflict between your divorce decree and the tax law. Under the tax law, you are the custodial parent because the child lived with you all year. Under the tax law, you can claim the child as a dependent. You do not need the mother's permission to claim the child. The IRS is not bound by your divorce decree, and the divorce decree cannot override the tax law. If you file your tax return claiming the child, the IRS will go along with that.
However, if you claim the child, you would be violating the divorce decree. The mother could take you to court for that, and ask the court to enforce the divorce decree.
You can give the mother permission to claim the child as a dependent by signing Form 8332 and giving the signed form to the mother. Doing that would satisfy both the tax law and the divorce decree. This would be the simplest way to resolve the conflict, but it means that you cannot claim the child. The court could probably order you to give the mother a signed Form 8332 allowing her to claim the child.
Even if you allow the mother to claim the child as a dependent, since you are the custodial parent according to the tax law, you could still use the child for the earned income credit and the child care credit, and to allow you to file as head of household, provided that you meet the other requirements for those benefits.
You should probably discuss the situation with your divorce lawyer.
