The child’s name does not determine which parent is eligible to claim an exemption for the child if the parents do not live together. As a general rule, the dependency exemption belongs to the custodial parent (the parent with physical custody of the child for the greater part of the year). The custodial parent may be the mother or the father. However, the custodial parent may waive this exemption in writing (and may be required by a divorce decree or other court order to do so).