This document seems to state HUDs current position on what the law is, pursuant to the Fair Housing Act and Section 504 of the Rehabilitation Act of 1973. There are two basic tests: Does the person have a disability, and do they have a disability-related need for a service animal? (It is allowed to request documentation of the claimed need for an animal, but not e.g. to inquire about the underlying reasons, thus a doctor could just write a note saying "Smith needs his ferret". Also, it is only allowed to ask for documentation if the provider does not already know, or cannot readily tell that the conditions exist). Assuming "yes" to both questions, the housing provider must "modify or provide an exception to a 'no pets' rule or policy". This is mildly confusing because HUD also declares that a service animal is not a pet, so what they must mean is that any policy excluding animals, including but not limited to pets, must be overridden. The "exception" holds
in all areas of the premises where persons are normally allowed to go,
unless doing so would impose an undue financial and administrative
burden or would fundamentally alter the nature of the housing
Denial of the exception is also allowed if:
1:the specific assistance animal in question poses a direct threat
to the health or safety of others that cannot be reduced or eliminated
by another reasonable accommodation
2:the specific assistance animal in question would cause substantial
physical damage to the property of others that cannot be reduced or
eliminated by another reasonable accommodation
There also cannot be any deposit required for a service animal.
It is noted that the Department of Justice has separate definitions, so pertaining to the ADA (DOJ's bailiwick), only a dog (or by a separate provision, trained miniature horses) can be a service animal, and this excludes emotional support animals. For an emotional-support ferret, the matter would come down to which law the facility is subject to.