Rejecting tenants based on their appearance

[Jim Bentley]

This question came up from reading http://www.biggerpockets.com/renewsblog/2013/01/27/tenant-screening/ on this site:

In that article, it advises landlords to check out a potential tenant's appearance, attitude, car, etc.

If I have a potential tenant who passes all of the checks (background/credit/previous landlords/etc.), but I don't like his looks (e.g. he looks like a creep, has a bad attitude, and his girlfriend has bruises, which I suspect he gave her) how can I legally refuse to rent to him?