Edit: I missed Fitz's post above.
I could be wrong here, but I believe that it's against the law to even ask if an animal is a service animal or not. Maybe that's just our corporate policy, but I've worked at a few casinos and it was the same deal at all of them.
"Don't ask. If the animal isn't housebroken or is aggressive toward other people, tell the person to remove the animal from the property. Otherwise, let them stay."