Tenant wants to add in husband with criminal record - need advice

Current situation, I rented a duplex out to a single mom with kids two months ago.  She's on section 8.  Section 8 pays 100% of the rent.  I received a letter from section 8 saying that she got married so she'll need to add her husband to the lease since he'll be staying with them at the duplex.  I took his application and ran it.  It has a long list of criminal history, from misdemeanor (battery, domestic, theft), to felony (stolen vehicle, drug...).  Some of which occurred last year.   

I'm not sure what do now.  I don't want to rent to him.  But at the same time, it's expensive to ask them to move and look for a new tenant.  Also, is it legal to deny the person base on criminal history? 

Thoughts?  Comments?