In the United States, a service dog that has been specifically trained to perform as part of a particular disabled person's "adaptive equipment" is required by federal law (Americans with Disabilities Act, or "ADA") to be admitted anywhere that the person is admitted. No one can refuse the dog any more than they can refuse a person's wheelchair.
The owner can sometimes get into a sticky situation if the dog prohibits the "normal and reasonable" course of business operations...ie: the person & dog get assigned an airline seat next to someone with a violent allergy to dogs. Or the person shows up ringside with the dog at the National Siamese Cat Specialty. In such situations, everybody has to help figure out Plan B. (Not that much difference, for instance, than an electric wheelchair that is simply too large to fit in the cabin of that same airplane.) But the service dogs have the same status as a guide dog--the normal "no dogs allowed" bans do not apply. Nor do the business owner's preferences that he'd really rather not have dogs in the store. Sorry pal. On the other hand, if the dog breaks something, makes a mess, bites someone, etc....the dog's owner is fully liable, not the business owner.
If you need a copy of the ADA law, you can obtain it from the web source noted below. We advise our clients to carry a copy of the law with them.