The second Q&A might help answer your question. From ADA.gov:
Q: How can I tell if an animal is really a service animal and not just a pet?
A: Some, but not all, service animals wear special collars and harnesses. Some, but not all, are licensed or certified and have identification papers. If you are not certain that an animal is a service animal, you may ask the person who has the animal if it is a service animal required because of a disability. However, an individual who is going to a restaurant or theater is not likely to be carrying documentation of his or her medical condition or disability. Therefore, such documentation generally may not be required as a condition for providing service to an individual accompanied by a service animal. Although a number of states have programs to certify service animals, you may not insist on proof of state certification before permitting the service animal to accompany the person with a disability.
Q: Can I exclude an animal that doesn't really seem dangerous but is disruptive to my business?
A: There may be a few circumstances when a public accommodation is not required to accommodate a service animal--that is, when doing so would result in a fundamental alteration to the nature of the business. Generally, this is not likely to occur in restaurants, hotels, retail stores, theaters, concert halls, and sports facilities. But when it does, for example, when a dog barks during a movie, the animal can be excluded.
