As a landlord, you certainly cannot turn prospective renters away because they have a disability. If you do, they could take you to court for discrimination.
Yet what if you are not turning them away out of malice but because you think your apartment will not be comfortable for them? Are you within your rights to do so?
Probably not. The law requires most New York landlords to make and pay for reasonable accommodations that someone with a disability requests to make living there easier.
Unless that is, you have an entirely different and valid reason for refusing to rent them the place, such as they have a record of trashing previous apartments or refusing to pay rent.
What is a reasonable accommodation for a disabled renter?
This is where it gets tricky. You probably cannot afford to spend half a million dollars making changes to one apartment for one client, and no one would expect you to do so. Yet how much is too much?
First, you should ensure you comply with anything required by the Americans with Disabilities Act, whether you have a tenant asking for it or not. Then you should look at what any potential tenant with a disability asks for on a case-by-case basis.
You probably need to make the accommodation if it merely requires you to modify your policy for them. If it requires you to alter the building, you need to consider the cost and how it affects the overall structure.
If you are unsure, seek legal help to assess your obligations as a landlord. It is easier than getting involved in a legal dispute because you refused to make modifications that a court would consider reasonable.