Qualifying tennants. Can I just say no?

[Fred Krueger]

Newbie question. When prequalifying possible tennants I am running into some seriously crazy people. I've been able to disqualify all of them due to income amount, credit score, etc... However, I'm wondering if I can disqualify someone based on gut feeling? If they meet the standards we've set but are just obviously not a good fit, can I just say no? How do you tell them that? What if that person is a protected class? Will they claim discrimination? Any help is much appreciated!