The divorce agreement might say something re who gets to claim the child. If this isn't the custodial parent, and the order is in 2009, the custodial parent has to sign a form 8332 and give it to the other parent. Often but not always, the claim is alternated between the parent each year.
The good news - if you are the custodial parent and are eligible for EIC, that stays with you, a judge can't give it to the other person even if the other person can claim the exemption. So if you're eligible, go ahead and file for that. Same goes for child care expenses if you had any so you could work. The only things the judge, or the form 8332, can affect are the dependency exemption and the child tax credit.
The good news - if you are the custodial parent and are eligible for EIC, that stays with you, a judge can't give it to the other person even if the other person can claim the exemption. So if you're eligible, go ahead and file for that. Same goes for child care expenses if you had any so you could work. The only things the judge, or the form 8332, can affect are the dependency exemption and the child tax credit.