IF the noncustodial parent qualifies they can claim:

• the exemption for the child (claim them as a dependent)
• the child tax credit for the child (up to $1,000)

ONLY the custodial parent can claim:

• head of household filing status due to that child
• earned income credit due to that child
• the credit for child and dependent care expenses
• the exclusion for dependent care benefits (i.e. from the W-2 form)

Per IRS Publication 17 Your Federal Income Tax, page 31:

Qualifying Child of More Than One Person

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, 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 exemption for the child.
2. The child tax credit.
3. Head of household filing status.
4. The credit for child and dependent care expenses.
5. The exclusion from income for dependent care benefits.
6. 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. The other person can't take any of these tax benefits unless he or she has a different qualifying child.

Tiebreaker rules. To determine which person can treat the child as a qualifying child to claim these six tax benefits, the following tie-breaker rules apply.

• If only one of the persons is the child’s parent, the child is treated as the qualifying child of the parent.
• If the parents file a joint return together and can claim the child as a qualifying child, the child is treated as the qualifying child of the parents.
• If the parents don't file a joint return together but both parents claim the child as a qualifying child, the IRS will treat the child as the qualifying child of the parent with whom the child lived for the longer period of time during the year. If the child lived with each parent for the same amount of time, the IRS will treat the child as the qualifying child of the parent who had the higher adjusted gross income (AGI) for the year.
• If no parent can claim the child as a qualifying child, the child is treated as the qualifying child of the person who had the highest AGI for the year.
• If a parent can claim the child as a qualifying child but no parent does so claim the child, the child is treated as the qualifying child of the person who had the highest AGI for the year, but only if that person’s AGI is higher than the highest AGI of any of the child’s parents who can claim the child. If the child’s parents file a joint return with each other, this rule can be applied by dividing the parents’ combined AGI equally between the parents.

Applying this special test to divorced or separated parents or parents who live apart. If a child is treated as the qualifying child of the noncustodial parent under the rules for children of divorced or separated parents (or parents who live apart), only the noncustodial parent can claim an exemption and the child tax credit for the child. However, only the custodial parent can claim the credit for child and dependent care expenses or the exclusion for dependent care benefits for the child, and only the custodial parent can treat the child as a dependent for the health coverage tax credit. Also, the noncustodial parent can't claim the child as a qualifying child for head of household filing status or the earned income credit. Instead, the custodial parent, if eligible, or other eligible person can claim the child as a qualifying child for those two benefits. If the child is the qualifying child of more than one person for these benefits, then the tiebreaker rules just explained determine whether the custodial parent or another eligible person can treat the child as a qualifying child.

See pages 31-32 of IRS Publication 17 for examples. Additionally, you can refer to IRS Publication 504 Divorced or Separated Individuals for more information about children of divorced or separated parents (or parents who live apart).