The only parent who has the automatic right to claim a child as a dependent is the parent the child lived with more than half the nights of the year. This is the custodial parent in IRS terminology. There is no such thing as 50/50 custody in a year with an odd number of nights, and the IRS does not follow state court orders.
If you are supposed to let the other parent claim your child, you have to give that parent a form 8332 dependent release. That form allows the other parent to claim the child tax credit. The ability to claim EIC, the child care credit, or use the child to qualify for head of household status always stays with the custodial parent and can't be waived, transferred, or shared. The other parent can't claim the child as a dependent without a signed form 8332 from you.
If you previously gave the other parent a signed form 8332 covering 2020, you can't revoke it now, it's too late. The other parent can claim the child.
If you did not yet give the other parent the signed form 8332 for 2020, the IRS won't care if you don't. The IRS will be perfectly happy to let you claim the child as a dependent. However, the family court in your state might be quite annoyed if you do not give the form 8332 to the other parent as ordered, and if the other parent complains, the family court can do nasty things to you, like reduce your child support, force you to sign the form for future years so you lose the dependent claim, or even toss you in jail for contempt. You should not ignore a court order without proper legal advice from your own attorney.
