Can I not schedule a tour if tenant doesn't pass my prescreening questions?

[Maya Jones]

I am new to this screening process, first time listing units in the market and getting request for tours. I have told everyone that before scheduling a tour we do a prescreening call. 
If a tenant, shows during prescreening call that for example they don't meet our 3x/rent income threshhold, can I go back to them and say we are currently scheduling showing for prospective tenants that meet our screening criteria. 
Is that legal and fair? I am in Chicago for reference

[Paul De Luca]

@Maya Jones

Yes, pre-screening is allowed and recommended before scheduling showings. If you showed your property to anyone you would waste a lot of time.

 You will quickly learn that even pre-screened renters are often flaky (won't show up or will cancel) or will not entirely be honest about things like their credit score. For this reason I recommend doing group showings for efficiency.

Personally I don't do a pre-screening call but make sure the renter states in writing that they meet the renter requirements. Don't just take them at face value for "yes, I meet the criteria". Ask follow up questions such as "can you confirm your credit score" or "what is your gross monthly household income", "when are you looking to move in?". I can't tell you the number of times someone has told me they meet the renter requirements but then they say their credit score is actually 500 and make below the minimum income amount. It may be more efficient to send renters a short form to fill out to avoid back and forth.

Make sure to apply your screening criteria to everyone equally and not violate fair housing laws.