The only way your situation as you described is legal, is if you and the other parent actually adjust the child‘s living schedule so that it physically lives in one parent’s home more than half the nights of the year, and the next year it physically lives in the other parent‘s home help more than half the nights of the year.
In that case you would switch from filing head of household with one dependent, to single with no dependents, and that will cause a very large swing in your tax bill and it would be a very good idea for you to file a new W-4 each January.
