You cannot do that.
The child can only be on one return - the credits cannot be split.
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 benefits between you. The other person can’t take any of these tax benefits for a child unless he or she has a different qualifying child.
The dependent interview is confusing since it asks about custody without really explaining what that means. That can lead you to answer the questions in a manner that gives credits to both parents when they both live with the child which is not allowed. The child can only be on one parents tax return and not on the other at all.
*Only* divorced or separated parents that have lived apart for the last 6 months of the year can have a *custody* agreement. The parent that physically lived with the child is the custodial parent and the parent that did not live with the child the non-custodial parent. Under those circumstances the custodial parent can release the child's exempt to the non-custodial parent who did not live with the child with a 8332 form (which is a custody agreement).
When *both* parents live with the child, no such custody agreement can exist since both parents have equal custody and there is no non-custodial parent. The dependent and all the benefits can only be claimed by one parent.