No. Landlords are not allowed to question you or any other applicant about a disability or illness, or even ask to see medical records.
Sometimes a landlord may think they're acting in the best interest of their potential tenants -- or protecting themselves from liabilities. However, even if it is obvious that you are disabled -- for example, you use a wheelchair or wear a hearing aid -- it is nevertheless illegal to inquire how severely you are disabled.
The policy behind this rule is simple: No matter how well-intentioned, the landlord cannot make decisions about where and how you will live on the property. For example if there are two units for rent -- one on the ground floor and the one three stories up -- the landlord must show both units to an applicant who uses a wheelchair, however reasonable he thinks it would be for the person to consider only the ground floor unit.