Can the noncustodial parent go behind custodial parent and claim EIC?

The noncustodial parent (NCP) is threatening to claim one of two children on his tax return to get the EIC. Custodial parent (CP) is rushing to H&R Block to get the return in before NCP has a chance to claim child #1. Will a tax preparer require special paperwork in a divorce scenario when putting children on the return for EIC? While the IRS flag NCP's filed tax return and deny him the EIC, while allowing the CP to claim the EIC for both children with no problems? Will there be an audit or investigation causing a delay in a refund? If so, would the delay be significant? Is there any way the IRS will accidentally approve the NCP's tax return and give him the EIC? Thanks!