The quick answer is no. According to the ADA, employees at a business "are not allowed to request any documentation" for a service dog.
The American Disability Act (ADA) prohibits both public and private businesses from discriminating against people with disabilities. In so doing, these businesses are required to allow people with disabilities to bring their service animals onto their premises wherever customers are allowed to go. Sometimes it is confusing if an animal is a pet or a service dog, and a business owner may wish to ask for documentation establishing that it is, indeed, a service dog. Is this legal? Absolutely. But that won't always help.
No Papers, No Problem
It's easy for business owners and patrons alike to be confused regarding an animal's "service" status, especially at businesses that have clear "No Pets" policies. After all, some, but not all, service animals wear special collars, harasses, or vests. Some, but not all, are licensed or certified, and actually have certification papers.
You can legally ask if the animal is a service dog animal required because of a disability. However, since certification isn't necessary for an animal to be a service animal, papers cannot be a condition for allowing the animal in. And in case you were wondering, disabled people are not required to carry documentation of their medical conditions or disabilities. So although it is legal to ask for service dog papers, it really doesn't matter.
Note, however, that service animals are not pets. Businesses are not required to abandon their "No Pets" policy. But they must make exceptions for service animals.
No Service, Big Problem
If a business refuses to admit a service animal for no justifiable reason, the business is in clear violation of the ADA. Justifiable reasons include:
Local and state health department regulations are trumped by the ADA, a federal law. So unless the animal is disrupting the establishment's business, or it is acting aggressively, businesses must let the service animal and its owner into any area of the business premise that other patrons can be, without charging any extra fees.
Refusing to allow access to a service animal can be an expensive mistake. Parkchester South Condominium, Inc, owner of a condo complex in New York City, had its security guard issue a 30 year resident a citation for owning a service dog, violating the ADA. In a settlement agreement, Parkchester paid the tenant $15,000 for emotional distress, the city $81,250 in penalties for willful violations of the NYC Human Rights Law, and a penalty of $10,000 for breaching a prior settlement agreement for a similar case.
If you feel that having a service animal in your establishment fundamentally alters your business, contact a local government agencies and programs lawyer, who can determine the legality of your belief before any expensive fines mount.
Editor's note, Sept. 2018: This article originally referenced outdated information by the ADA. It has since been updated to reflect the most recent ADA guidelines.