I'm not sure of the legality of not allowing a service animal. I'm pretty sure you have to by the ADA laws. If they do need a service animal, they'll have documentation. Don't let them try to trick you into thinking they need it and they don't have any papers on it. They don't carry these papers around at all times, hence why you don't see people ask for it in the store or anything. If they are renting your place, however, they will likely have papers showing that is not a pet, but a service animal. If they don't, ask them for a reference of a doctor or someone you can personally verify they need this animal with.