Americans with Disabilities Act (ADA) is the federal law that guarantees the right for a disabled person to have access to public places for their dogs.
State laws may broaden the rights guaranteed under the ADA but they may not restrict the rights. For Wisconsin state laws
There are three types of Assistance Dogs: Guide, hearing, and service dogs.
Service dogs are trained to perform a specific task directly related to the person’s disability. Although guide and hearing dogs are service dogs, the term service dogs also applies to dogs that are specifically trained to provide a services to physically disabled people other than the blind or deaf. The disability of the person may not be recognizable. For example, a person with seizures may have a dog trained to sense the warning signs of the seizure, or protect the person while they are seizing.
Psychiatric Service Dogs are covered under the ADA as long as the dog is trained in a specific task related to the disability. Examples would be providing safety checks or room searches for a person with PTSD, or preventing or interrupting behaviors such as self-mutilations.
The provision of emotional support, well-being, comfort, or companionship does not constitute work or tasks for the purposes of the definition of a service dog by the ADA.
Although Emotional Support Dogs do not qualify as service animals under the Americans with Disabilities Act (ADA), they may be permitted as reasonable accommodations for persons with disabilities under the Fair Housing Act. The Air Carrier Access Act provides specific allowances for ESAs traveling on airlines, though documentation may need to be provided.
Therapy dogs provide a service to people in nursing homes, hospitals and schools bringing them comfort and cheer. They are not service dogs or assistance dogs. They are not covered by the ADA and do not have public access rights provided to assistance dogs.
Under the ADA and Wisconsin law a public accommodation may not ask you questions about your disability or demand to see certification however they may ask if your dog is a service dog and what service it performs.
A service dog is trained to assist a disabled person, but first it is trained as a well behaved dog. When not performing that assistance they are taught to be quiet, not bark or growl, and they are never disruptive.