There is a big difference between a “companion animal” and a “service dog.” Service dogs undergo special training (such as seeing eye dogs, or seizure dogs) and have special laws that protect them and their owners. Companion animals are pretty much a made-up concept that only has any legal basis for airlines and only require a certificate that can be bought online without any validation. I could dig a worm out of the garden and print out a “companion animal” certificate from a website. Unless you’re an airline, it’s not required to give any sort of special status to a companion animal.
It is my understanding that you can tell someone in your store with a “companion weasel” to get the fuck out. Furthermore, if you don’t kick them out, and the guy’s “companion weasel” bites another customer, you can be liable for not exercising reasonable precautions in protecting your customers. This isn’t legal advice. I am not a lawyer.