You cannot discriminate against him for anything that is a protected class- race, religion, etc. If you are not violating those laws and you simply want to rent to someone else over him because- for example he is an obnoxious person who is threatening you with lawsuits or because he simply doesn't have a credit score that is acceptable to you as the unit owner- you do not have to rent to him and there's nothing he can do.
He could attempt to sue you for what is called specific performance which would be basically asking the courts to force you to rent him the place but you have no contract and I've never heard of that happening in a rental situation.
As always, consult with your attorney but it sounds like you've done nothing wrong and have nothing to worry about.
Separately, I suggest you use consistent practices with tenants. Credit report, written application, references, are all normal. The key is showing that you treat all candidates. But you are perfectly entitled to ask away.
Best of luck,