You are not allowed to claim the child/dependent care credit (DCC) for a child that did not live with you for more than half the year.
If you are not the custodial parent (the IRS goes by physical custody, not legal custody), you cannot claim the DCC even if it is your year to claim the dependent. The other parent can count the money you paid in claiming the credit for herself.
If you are the custodial parent, you enter the child in the personal info section as a dependent. The interview will ask you if you are allowing the other parent to claim the dependency. After answering yes, it will allow you to claim the child as a non dependent (for the EIC and DCC). You can count the money the other parent paid (it is treated as child support).
There is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/exemption/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner.
Note in particular that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has released the dependency to him.
