The custodial parent is the "filer" of the 8332. They would fill out this form IF 1) they are releasing their claim to the child to the noncustodial parent in a given tax year, OR 2) to revoke any prior/future release of their claim to the child for tax purposes. If you are the noncustodial parent who is claiming the child for 2020, the custodial parent (assuming this is who you are referring to when you say "the other parent") would be the one to fill this out and file with their return. Then, once the IRS receives both returns and verifies that the custodial parent has, in fact, released their claim, then return will be processed. In past, there have been many instances where the noncustodial parents' return has been processed without this electronic verification, however, when the custodial parent files - and there is no 8332 release of claim filed along with it, a letter would go out to both parties indicating this along with instructions to follow to correct the error.
