If a person wants to bring their dog into a public place, the only questions allowable are, “Is that a service animal?” and, “What task does s/he perform?” Asking about the person’s disability or requiring to watch the animal perform the task are in violation of the person’s rights.
No, there is no federal requirement for the dog to wear any special gear or identification. There is also no requirement that the handler carry any certification papers showing that the animal has been trained for service. Some service animals may have certification from a professional trainer, but many are trained by their handler.
If you operate a business open to the public, you must permit a person with a service dog to have access. Reasonable accommodation must be given to the disabled person. For example, if a service dog must enter a business at the same time as a person who is allergic to dog dander, they should be assigned to different locations within the building.
Explain to your customers that the service animal is medically necessary and that federal law permits people with service animals to have access to public places.