No.
Only the custodial parent can claim the Earned Income Tax Credit, the Child and Dependent Care Credit, as well as possibly claiming Head of Household filing status.
"If the custodial parent
releases a claim to exemption for a child, the noncustodial parent may claim
the child as a dependent and as a qualifying child for the child tax credit.
However, generally, the noncustodial parent may not claim head of household
filing status or the earned income credit, and the noncustodial parent may not
claim the credit for child and dependent care expenses, the exclusion for
dependent care benefits, or the health coverage tax credit."
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