When 1 out of 4 girls & 1 out of 6 boys are sexually assaulted by their 18th birthday, there are a TON more sex offenders out there than what state websites show, because most are never caught & convicted. 

My wife volunteers at a women's crisis center that deals with sexual violence.

Many people don't know that in addition to national fair housing law, states and municipalities may have additional protected classes (for example, in Austin TX we have local additions to fair housing that cover sexual orientation, status as a student, and others)There are resources from the national apartment association (and through many state and local associations) specifically geared to educating and supporting independent rental owners (usually regarded as having less than 100 units).  

Most felonies are as well, especially those of a violent or sexual nature.

What if the prospective tenant takes the key and then drags some lady into the property and sexually assaults them? 

If it's riddled with murder, rape, sexual assault.......or are they all minor drug charges....

You should get credit, criminal, sexual predator, homeland security and verification of identity.  

However recently crimes such as armed robberies and home invasions have been getting more common in tourist areas as well, especially Quepos and Puerto Viejo (which has a major problem with sexual assault). 

Make a policy that is identical for RACE as it is to AGE, SEXUAL PREFERENCE, LAWFUL OCCUPATION... etc. 

They are not allowed to discriminate based upon race, color, creed/religion, sex (though it does not state it, I am assuming this includes sexual orientation), disabilities, familial status, or national origin.