Congressional Research Service (CRS) serves as nonpartisan shared staff to congressional committees and Members of Congress. It operates solely at the behest of and under the direction of Congress. They recently posted a summary of laws dealing with service and assistance animals.
The three main laws concerning service and assistance animals for the disabled are the Americans with Disability Act, the Air Carrier Access Act and the Fair Housing Act. The Americans with Disabilities Act covers access to businesses and other public services. The Air Carrier Access Act specifically addresses airlines (as opposed to airports covered by the ADA), and the Fair Housing Act concerns non-commercial housing and covers property owners, housing managers, HOA's, insurers, real estate agents, housing authorities, and colleges and universities. All three acts state that businesses and services must make "reasonable modifications" to policies, practices, and procedures.
According to the ADA, a disability is a physical or mental impairment that significantly limits one or more major life activity. The ADA and the ACAA only protect service animals -- those animals trained to do work or perform tasks specifically related to the disability. Only dogs and miniature horses are covered by ADA and ACAA. Miniature horses may be used by people who are allergic to dogs. No peacocks need apply. Emotional support animals are not covered by these acts, but trained animals providing psychiatric assistance are.
Businesses may not ask a person what their disability is, but they can ask what the animal has been trained to do. Airlines may ask for DOT (Department of Transportation) forms concerning the health and/or training of the animal. Animals must always be under the control of the handler, who must provide care and clean up.
The FHA does protect assistance animals as well as service animals, including untrained ones, although the housing provider can still ask about the animal's function and for verification and documentation. Common household animals (dogs, cats, etc.) are protected, but barnyard and exotic animals are not without documented proof of need. Housing agents must allow the animals, but owners are liable for the cost of any damages caused by the animal.
The HUD says that denials of assistance animals accommodations are rising and are one of the most common fair housing complaints.
Other acts that include information about service and assistance animals are the Rehabilitation Act of 1973, the Affordable Care Act, the Congressional Accountability Act, and the Individuals with Disabilities Education Act.