Though there is nothing saying you have to allow just anyone to have pets, there are laws in place that involve protections of the disabled and often, the elderly, in respect to their pets.
There are a few things that should be fairly common sense. Tenants who reside in federally assisted housing for both the handicapped and the elderly are allowed by law to keep pets. Even if the property isn’t owned by the government, if it’s being subsidized, those groups have a protected right to keep their pets under Housing and Urban-Rural Recovery Act of 1983, 12 U.S.C. section 1701r-1. Management and property owners are allowed to have reasonable regulations in place, but if your property is a HUD property, there’s a good chance that it’s covered. You may want to check with the local HUD department or even your local Housing Authority- but this holds true in many cases.
For instance, in California, if a property is owned and operated by local state, county, or city or even district agencies, apartment dwellers over the age of 60 or who are disabled are legally allowed to have two small pets in their apartment. Several other states have similar rules. The District of Columbia, Arizona, Massachusetts, Minnesota and New Hampshire, for example. In Massachusetts, one dog under 40 pounds is allowed, as long as it has been spayed or neutered.
Whether or not state law covers it, if you are a recipient of federal money: you have to make reasonable accommodation for your disabled tenants. What this means is, if someone has a therapy pet and it would cause no hardship for your property: this is a reasonable accommodation you have to concede. That does not mean you are without recourse, should the animal cause a problem. In some cases where the animal is not properly cared for or causes property damage, an eviction may be upheld.