I got a question from a reader who saw the prior blog entry concerning criminal background checks.  The reader asked if management can just randomly pick and choose as to which applicants they run background checks on.  In a word, the best practice is, simply no.
In a world filled with litigation generally and Fair Housing Act cases specifically, even if your motives are pure and you only want to randomly select certain applications for criminal (and/or credit) screening, you subject yourself to unneeded potential scrutiny because someone in a protected class (whether an applicant or a fair housing tester) may challenge your claim and say that management only screened members of a certain protected class to keep them out of your community.  And if a complaint is filed, you will be forced to attempt to explain why and how the specific files were selected for screening while others were skipped.  And if the investigator finds a pattern of excluding some classes, you will really need a lawyer like me.  
Bottom line:  Management should absolutely have a criminal background and credit screening program in place.  And you should run it on every applicant.  No exceptions.
Just A Thought.