The US Constitution states (well, the Constitution as interpreted by the US Supreme Court) that you can't discriminate against certain classes of people, which includes "protected" classes based upon (as best I can remember) race, religion, sex, national origin, age, and disability. So, I think (but I'm not sure) that they might be able to refuse to rent to tatooed people (or anyone), as long as it isn't a hidden reason ("pretext" in legal terms) for refusing to rent to someone who is in a protected class.
They are really treading on thin, "legal" ice by classifying people into a group for the purpose of denying them access.
