Q. When the wording in the official child support order gives the non-custodial parent permission to claim one child as an exemption* for income tax purposes, is this to imply that the earned income tax credit (EITC or EIC), is also something that non-custodial parent is permitted and allowed to claim.
A. No. But it does mean he can claim the Child Tax Credit (CTC). The CTC essentially "goes with" the exemption. Even if the court order specifically says the non custodial parent gets to claim the EITC; that provision would be invalid, as federal law does not allow that.
*Prior to 2018, "claiming the exemption", meant getting an approximate $4000 deduction (it went up a little each year). The exemption deduction was eliminated starting in 2018. It was replaced by an increase in the CTC, for children under 17, and a $500 Other dependent credit for others. So, if you court order says you can claim the exemption, it means you can claim the dependent and the CTC or $500 other dependent credit.
