Quote from @Ryan Bird:
Great! Can we ask their credit score in pre-screening?
I have been using Zillow to screen my tenants and it gets most of the basic stuff out of the way, criminal history, credit score, rental history, a few basic questions, and has great visibility. You definitely want to come up with your own questionnaire to help get a feel for who they are and how they will be as a tenant. I wouldn’t just ask about their credit score or any of the sensitive subjects, they probably don’t want to talk about it anyway and frankly I don’t want to have the conversation. In conclusion, use a screening service to prequalify them and then move on to step two of having them fill out your own application. Show them the respect of including your requirements in the ad so that they don't spend $30 on the screening when they know that they won’t qualify.
As far as denying them, it’s usually just “ I’m sorry but you don’t meet our _______ requirement.” And that’s the end of it.
Hope this helps.