No there is no law requiring that the claim be alternated. If the agreement was ratified by a court, then you'd have to get that undone. If what you signed was a form 8332, then you can sign another one revoking the previous one - it won't take effect until next year though.
If he doesn't have either a valid court order or a signed 8332, then you as the custodial parent get the claim. Even for years though when he claims the child as a dependent, you can still get EIC, child care credit, and head of household status if you qualify for them, he doesn't get those based on your child.
Child of divorced, separated or unmarried parents: Only the custodial parent can claim the child. It does not count who is paying child support. The custodial parent is the parent with whom the child lived for the longer period of time based on the nights spent.
The other parent is the non-custodial parent. Non-custodial parent can claim the child only if the custodial parent signs a release Form 8332 or there is a court order meeting the IRS requirement. With form 8332, the noncustodial parent gets exemption deduction and child tax credit, but not the head of household status.
Even after signing Form 8332, the custodial parent is head of household and get EIC and any child care credit.
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