Only the custodial parent, with whom the child lived with more than half the year, can claim Earned Income Credit, Child and Dependent Care Credit and the Head of Household filing status.
A non-custodial parent can claim his or her child as a dependent if the custodial parent has signed either a Form 8332 or a similar statement.
If the non-custodial parent is able to claim his or her child as a dependent, the non-custodial parent will get the dependent exemption as well as Child Tax Credit.