As I have written before, it goes without saying that management should run a non-discriminatory criminal background and credit screening check on all of our applicants for housing.  Doing so makes good business sense and helps ensure the safety of our residents as well as the management team.
What happens if an applicant has a criminal history as well as a disability?  The applicant will state that he or she needs a reasonable accommodation because of that disability.  In support of such an argument, tenant advocates will contend the Fair Housing Act (FHA) has been (or will be violated) if the reasonable accommodation request is denied based on a criminal record if the prior criminal activity was related to a disability. 
At least one federal court has held that a landlord did not need to provide an accommodation in the application context where the housing denial was based on a facially neutral policy which rejected the applicant with a criminal record related to violent crime. See Evans v. UDR, Inc., No. 7:07-CV-136-FL, 2009 WL 1026724 (E.D.N.C. Mar. 24, 2009).  The court concluded that the requested accommodation (in this case for a mentally disabled applicant who was denied an apartment) was not an issue in the case as the applicant was denied because of her criminal background. The FHA was found not to provide protection for those with a criminal history and that management had no obligation to make an exception because the applicant was also mentally disabled.  In other words, the court noted that these are separate issues — and the landlord has the right to have a “no criminal history policy.”  On the other hand, because nothing is ever easy, a different court in Boston Hous. Auth. v. Bridgewaters, 452 Mass. 833 (2009), found that the resident was entitled to a reasonable accommodation after receiving an eviction notice based on a criminal history.
My usual advice in this situation is to develop and put in place a reasonable criminal background policy that you feel appropriate.  What is important is to apply it across the board and not make exceptions.  I am defending against a case right now involving these very issues.  I will let you know how it turns out.  
Just a Thought.