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"custodial parent" should be considered an IRS term. it's the parent the child lives with for more than 183 nights.

you say the child is with dad. thus, I assume that's more than 183 nights making him the custodial parent in the eyes of the IRS. the IRS doesn't care what the courts say or what you agree to.  only the custodial parent can claim the child unless they furnish the non-custodial parent with a signed form 8332 which the non-custodial parent must include with their tax return. this means that the non-custodial parent will have to mail in the return.

 

Post-1984 and pre-2009 decree or
agreement. If the divorce decree or
separation agreement went into effect after
1984 and before 2009, the noncustodial
parent can attach certain pages from the
decree or agreement but these pages must contain ll the info required by the form.