If you have a court order requiring you to let the non custodial parent claim the child then you must comply or be in contempt of court. Complete & deliver the form 8332 as directed by the court to stay out of jail.
IRS rules on custody ...
The
parent with whom the child lives more than half the year (184 or more 184
nights for 2016) is automatically entitled to claim the child as a dependent.
This is the custodial parent. (IRS determines custody based on where the child
lives, not any court order or agreement.) The non-custodial parent is
not entitled to claim anything.
However,
the custodial parent can sign a release (form 8332) allowing the non-custodial
parent to claim the child as a dependent. You can download this form from
the IRS web site. The custodial parent signs it and gives it to the
non-custodial parent and the non-custodial parent mails it to the IRS after
e-filing the rest of their tax return.
In this case, the non-custodial
parent can claim the dependent exemption and the child tax credit. The non-custodial
parent can never claim earned income credit, the dependent care credit (day
care credit) or use the child to qualify for head of household status.
Those benefits always stay with the custodial parent.
