Can one non-married parent claim a dependent while the other parent has FSA dependent care for that child? Both parents live together with the child.

No unmarried parents can't split the benefits for a child. One parent gets all, the other parent gets nothing.

It is a decision that the two of you decide together assuming you each meet the qualifications. Sometimes a child meets the rules to be a qualifying child of more than one person. If the child is the qualifying child of more than one person, only one person can claim the child as a qualifying child for all of the following tax benefits:

• EITC,
• Dependency exemption for the child,
• Child tax credit,
• Head of household filing status,
• Credit for the child and dependent care expenses, and
• Exclusion for dependent care benefits.

The other person(s) cannot take any of the six tax benefits listed above unless he or she has a different qualifying child. If they cannot agree who will claim the child as a qualifying child, and more than one person actually claims tax benefits using the same child, the tie-breaker rules (explained below) apply. If the other person is a spouse and they file a joint return, this rule does not apply