There is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/exemption/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner.
Note in particular that the non-custodial parent can never claim the Earned Income Credit (EIC), Head of Household (HoH) filing status or the dependent care credit (DCC), based on that child, even when the custodial parent has released the dependency to him.
Even though the child is not listed as a dependent on the Mom's tax form, she may have used the child for EIC, HoH, and/or DCC. If you also try to claim these items, your e-file will be rejected.
Ref: https://www.irs.gov/publications/p17#en_US_2017_publink1000170897
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For tax purposes, there is no such thing as joint custody, regardless of what your legal agreement says. The requirement, to be custodial parent, is that the child live with you MORE than 50% of the time. One of you has to be the custodial parent and the other the non-custodial parent. The IRS goes by physical custody, not legal custody. The custodial parent is the parent the child lived with for more than 182 nights in 2019.
It is allowed for you to arrange the children's schedules so that the child spends more than half the year with the father one year and more than half with the mother the next year so that you are each the custodial parent in the year you claim the child, so that you can claim full benefits.
