IRS Pub 501:

Sometimes, a child meets the relationship, age,
residency, support, and joint return tests to be a
qualifying child of more than one person. Although

the child is a qualifying child of each of
these persons, generally only one person can
actually treat the child as a qualifying child to
take all of the following tax benefits (provided
the person is eligible for each benefit).
1. The child tax credit or credit for other dependents.
2. Head of household filing status.
3. The credit for child and dependent care
expenses.
4. The exclusion from income for dependent
care benefits.
5. The earned income credit.
The other person can’t take any of these
benefits based on this qualifying child. In other
words, you and the other person can’t agree to
divide these tax benefits between you.