There are special rules for your situation:
For divorced or separated parents or parents who live apart, the custodial parent, if eligible, or other eligible person who the child lived with for more than half the year, can claim head of household filing status, the credit for child and dependent care expenses, the exclusion for dependent care benefits, and the earned income credit.
The non-custodial parent, if allowed by divorce decree or consent of the custodial parent on form 8332 or similar signed statement, can claim the dependency exemption and child tax credit. For post-2008 divorce decrees or agreements, form 8332 or similar signed statement is required. The child tax benefits cannot be split any other way.
