It is up to the individual apartment company & their rules; there is no law about it. (The only law is if they use a company to run criminal checks, the company is prohibited from going back more than 7 years.)
If you cannot find a place that is run by a large company, you should try finding a place owned by an individual with whom you can talk and explain. (You might provide a copy of your judgment on your case.)
I doubt there are any state laws prohibiting apartments from renting to convicted felons. Most likely, an apartment's decision to not rent to a convicted felon is based on their business model - they want to promote a certain image to their residents. You should just ask the prospective apartments that you are interested in renting whether this issue will preclude you from being allowed to rent with them.
Attorney's answers to questions are for general purposes only and do not establish an attorney-client relationship.
It is legal for them to deny your application due to your rental history. It's up to each company to make their own policies on this issue. It may be harder for you to rent, but you'll find a place.
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