I also don't want to be housing a convicted rapist, thief, drug dealer, etc.

If anyone thinks a judge or any jury does not impose thier moral convictions in a court of equity they must be asleep

Here's some tips for niche list acquisition and ideas: Debt Claims, Divorce, Evictions, Felony Convictions ,Foreclosures, Probate, Small Claims, Tax Delinquencies, Tax Exemptions, Vacant Properties, code violations.Here's some of the sources that you can utilize if you'd like to get ahead of those using the same data solutions (i.e.. listsource/propstream).

Was it a felony charge or conviction?

Make a specific criteria for renting your property (Credit score, DIR, No evictions, Criminal convictions etc) and stick with it. 

I ask; When are you looking to move, how many people would live there, do you have any pets, do you meet the criteria of 600 credit score, 3 times income to rent, no felony convictions, and no evictions, and are you willing to pay a $40 application fee for all adults to check that list? 

With that being said, I'm working on my Pre-Qual questioning; my question is, can you ask if someone is a convicted felon, and is it legal?

i have personally never had that offer when it wasn't to compensate for some sort of red flag, ie: past evictions, felony conviction, sex offender, drug dealer, or prostitution/porn But who knows, there's a first for everything!

I have an applicant who has a relatively recent history of two domestic battery arrests but no convictions.

He mentioned to me that it wasn't pleasant.The online screening service did not show any convictions.