You are allowed to ask if it is a certified service animal or comfort animal. If it is a certified service animal, then that is all you need to know because you are venturing into their private health info. If it is a comfort animal, which is not a licensed animal beyond a pet, you are st liberty to decide whether or not that animal is allowed. Service animals are afforded all the same rights and access to businesses as people, as long as they are certified to perform multiple trained tasks related to that person’s disability and quality of life. Only a law enforcement officer can ask for the service animal’s owner to rovide proof of what they are capable of. It is no different then you walking up to a person in a disabled parking stall and asking for proof that they are really disabled. As a business owner, all you need to know is that they have a permit. If you doubt that they are disabled, a law enforcement officer can be called to question them, but can not do anything beyond verify they are the person and that a doctor signed the paperwork.
Disabled people have rights to privacy and if their animal is certified as a service animal by the government and a doctor, that is all that a business owner needs to know. If that dog is misbehaving, aggressive, or not housebroken then you are allowed to ask them to remove the animal. A legitimate service animal is bo different than a cane, wheelchair, or any other tool used to help a disabled person function.