If you are the custodial parent, you are entitled to claim her on your return.As non-custodial parent, her father cannot claim her unless you release your claim by providing her father with a signed Form 8332. He must attach this release to his return to claim a child that does not reside with him.
Those are the tax rules. But what is probably going to happen is - his return will go through with your child on it. If you e-file your return with your daughter also claimed, your return will be rejected. The computer knows your child has already been claimed. It does not know you are entitled to the exemption.
The best course of action, is to complete your return as you normally would. Do not take into account what he has done on his end.
You must print and mail your return into the IRS. Include a statement explaining you are custodial parent and have not released your right to claim, you have not given your daughter's father the Form 8332. He will get a notice correcting his tax return.
Alternatively, and depending on your situation, you may choose to discuss this with him. If he doesn't want the IRS to clear it up, he can amend his return to remove your child. Once he receives notice that his amended return has been accepted, you can file as you normally would.
