If all other checks look good (credit, criminal, eviction, landlords, etc.) then it might be worth taking them as a month to month tenant only.  

I use TenantBackgroundSearch.com and the site emails the tenant for authorization to run the credit/criminal search.  

When I add a tenant  I do a criminal  back ground check at very  the least .

I check 4 main areas: credit report, court records (criminal & evictions), income, and land lord references.I don't look for a specific credit score.  

.- An income to rent ratio over 3:1- Passed criminal background checkIt's a 3 bd/2ba property and the applicant is a single adult.

First one's results came back, all clear everything, no criminal, evictions, etc.

It also gives us criminal background and eviction info and everyone else goes through the exact same checks.

You don't want someone calling your name in a civil or criminal suit as the person who knew about the problem, had the power to take action, but chose not to. 

Either way, it is risky to deny an applicant soley based on past criminal conduct.Good luck!

http://money.cnn.com/2016/06/22/technology/airbnb-...from the article"This week, Los Angeles started to take action against rent-controlled apartments that have been illegally converted into short-term rentals The city filed criminal charges against the Farifax building's owners and civil cases against three other building owners.