When selecting a tenant, there is more than meets the eye.  You should do a credit check and a criminal background check.  However, more often than not, the credit score may not be that great.  Look further, see what caused that.  If there was a prior eviction, then, of course, do not rent to them.  If they did not pay their utilities, do not rent to them.  However, if it is a credit card that was past due, see what it was all about.  Sometimes the tenant has good character and made poor choices with their credit card.