What is the penalty if the non-custodial parent and the custodial claims a child on their taxes?

The mother (custodial parent) has all of the necessary documentation to show that she was the primary supporter. Will the father be penalized?What is the penalty if the non-custodial parent and the custodial claims a child on their taxes?
When a second return is submitted with the same dependent, both returns are flagged for review. The taxpayer who was not entitled to claim the child will have to redo his/her tax return. If the taxpayer was due a refund (after the recalculation), there will not be a penalty. However, if the taxpayer will owe money, there will be a penalty for not paying the full amount of taxes due by April 15.