You do not need form 8332, if the "child" is emancipated.
However, you may still need the parent's verbal permission, if the child still lives with his parent and otherwise meets the Qualifying Child rules (mainly the child is a full time student) for that parent. That is, you need to be sure the other parent isn't claiming the child. Even then, technically you may not be able to claim him.
If there is a conflict, the other parent has priority, regardless of the amount of support you provided.
