The simple answer is no. According to the U.S. Department of Justice , businesses and organizations that serve the public have the right to ask a person who has an animal if it is a service animal. However, since the Americans with Disabilities Act (ADA)  does not require that service animals be licensed or certified, they may not insist on proof of certification before permitting a service animal to accompany a person with a disability. A service animal, however, may be excluded when its behavior poses a direct threat to the health or safety of others.
Further discussion related to service animals can be found in the U.S. Department of Justice's Commonly Asked Questions About Service Animals In Places Of Business  and the ADA Business BRIEF: Service Animals .
-  U.S. Department of Justice
-  Americans with Disabilities Act (ADA)
-  Commonly Asked Questions About Service Animals In Places Of Business
-  ADA Business BRIEF: Service Animals