My child lived with me 6 months last year, Can I claim her on my taxes?

Child of divorced, separated or unmarried parents:
Only the custodial parent can claim the child. It does not count who is paying child support. The custodial parent is the parent with whom the child lived for the longer period based on the nights spent. The other parent is the non-custodial parent.
Non-custodial parent can claim the child only if the custodial parent signs a release Form 8332 or there is a court order meeting the IRS requirement. With form 8332, the noncustodial parent gets exemption deduction and child tax credit, but not the head of household status and EITC.
Even after signing Form 8332, the custodial parent is head of household and get EIC and any child care credit. Your U.S. Tax Return: Child of separated or divorced parents