Felony history with a tenant

[Dave Derocher]

I just received an application from a couple and they noted that they have been convicted of a felony.  As they were filling out the application in front of me they both told me about their own felony in the past.  The male had 9 felonies all more than 12 years back, and she has a possession felony that she is on probation for (about 1 1/2 years ago).  They both shared freely this info I didn't ask for any explanation, I assumed it would show on the background check.  When doing the background check through Smartmove,  nothing came up for either of them.  I'm pretty sure i want to decline them as i believe the market is strong in the area.   

My questions is can I decline them based on what they told me even those it's not in their background check and how do i word it in the decline letter.  After reading many forums on BP i haven't gotten a really clear answer as to if this is discrimination or not.  Even going through the State of Michigan landlord material i haven't really gotten a clear answer.    This is the first denial i have done, and don't want to open my self to legal issues.  

Dave 

Freeland, Michigan