If you have custody more than half the nights of the year, and neither of the parents had custody for more than half the nights of the year, then you are the only person allowed to claim the child.
If the parent does claim the child and e-files first, you will be blocked from e-filing. Just print your return, sign it, and mail it in.
The IRS will eventually investigate the duplicate claim. You may need to show proof that the child lived with you. The IRS especially likes proof from trusted third parties, like letters sent to your home address from the child's doctor or school, that show that the child was living in your home. If this is a court or foster placement, that's also good proof.
