Who Files taxes when parents are separated can not come to a agreement

The IRS cares about physical custody.   If the other parent already filed a tax return and claimed the child, your own return will be rejected when you try to e-file with the child's SSN on your tax return.   So.....file your return by mail. The IRS will handle and process that return differently than an e-filed return; they will sort out which parent could claim the child.   If the child was claimed by a person who should not have claimed the child, that parent will face repayment of any child-related credits they received plus penalties.

As far as the IRS is concerned the custodial parent is the one with whom the child spent t least 183 nights during the year.

There are some parents who live apart that "share" the child-related credits with a signed agreement---form 8332.   But if you do not have such a signed agreement, you do not have to give up any of the child-related credits.

When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s.  Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS/state received the return.

Federal and state returns must be in separate envelopes and they are mailed to different addresses.  Read the mailing instructions that print with your tax return carefully so you mail them to the right addresses.