I saw a leashed dog in the library and saw no obvious identifiers that it was a service animal. I approached the patron and told him that pets were not allowed in the library. He told me that if I looked down, I could see it was a service animal. In fact, I could not. He then turned the animal around and pointed at the collar, which had "service animal" embroidered in it.
First, I want to be very clear that service animals (dogs and miniature horses) do not have to wear any specific collar or badge. It is by their training and the service they provide (often not easy to discern to a casual observer) that they are identified. For that reason, it can be easy to mistake a service animal for a pet, so caution is always warranted.