You'll file a paper return and claim the child as a dependent (the IRS will reject an e-filed return once her SSN has appeared on another return). Then, since two returns are showing her as a dependent, the IRS will send letters to each of you asking for a statement/documentation to support the dependency exemption. After receiving the responses, they will render a decision.
If you are the custodial parent -- meaning she has lived with you for more than half the year -- then your ex would need your signed permission (Form 8332) to claim her as the non-custodial parent.
