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@DCTAXPRO wrote:

She just doesn't qualify for EITC because of the tie-breaker rules.

Where does is state that the MN Child Tax Credit only goes to the custodial parent?

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The tie-breaker rules don't apply if they agree to who can claim the child.

If they agree that she can claim the child, she can also claim the Earned Income Credit.  If they both claim the child, he would 'win' and she couldn't even claim the child at all (she wouldn't get the Child Tax Credit).

Is he trying to claim the child in any way, such as for Head of Household?

The Instructions that are part of the form says that Form 8332 does not qualify for the credit.