Thanks, garman22.  The mom needs the base refund to help with her costs, so I'm leaning towards filing as single instead of HoH, with no dependents...aargh.  The separation agreement does not mention the father claiming the child and there is no F8332 on file.  The joint custody agreement indicates that the JCA is continuing with prior practice between the father and the mom and the mom has the child 137 night each year.