No, a business cannot ask to see proof, documentation, certification, or identification that your dog is a service animal under federal law.
The U.S. Department of Justice's ADA guidance explicitly states that businesses and public entities cannot require:
Medical documentation
Proof of training or certification
A special ID card, registration, or license for the dog
The dog to demonstrate its tasks
When it's not obvious that the dog is a service animal (e.g., not visibly guiding a blind person), staff may only ask two questions:
Is the dog a service animal required because of a disability?
What work or task has the dog been trained to perform?
They cannot inquire about the nature of your disability, demand proof, or require a vest/harness.
While some states penalize faking a service animal or have rules for animals in training/housing, no state requires documentation or ID for a fully trained service animal in public places.
Practical note: Many handlers use vests or patches voluntarily to signal the dog's role and reduce questions or challenges.