There is no agency that regulates service dogs. There is such thing as a doctor writing a prescription for a dog, but that's meaningless from a regulatory standpoint. So is a certificate from a training school. Same with a vest. The agency you can get in trouble with if you deny someone access to their establishment is the ADA.
Per the ADA the only questions the owner of an establishment can ask are these:
Is this a service animal?
What does it do for you?
You can't ask for a demonstration and you can't question the persons answers if they say yes.
Someone mentioned Vets and "comfort dogs" I think what you meant was "psychological service animal" because a "comfort dog" has no special training. Psychological service animals are trained to patrol the area around the person so that they feel safe, to "get [my] back" by standing or sitting behind the person when they feel exposed, like at an ATM, or to just generally create space between the person and a crowd. Some are trained to growl on cue in the event of a threat (they're not attack dogs, though.) Dogs can also benefit Vets by encouraging social behavior- responding to questions about their dogs and meeting people who are interested in service animals.
I have a pretty strong opinion that service dogs need to be regulated- both to get rid of fake service dogs and to make sure that real service dogs are trained properly The idea that "he's a service dog if I say he is and you can't disagree of I'll sue" creates animosity between business owners and people with disabilities. The fakers also make people with genuine physical and psychological disabilities look bad and possibly be less likely to adopt a dog that could help them a great deal.
