Service dog documentation is NOT required. To ask for it is not legal. However a service dog can be prohibited if it does not have a rabies tag, or other locally required licenses (varies from community to community.)
Please see questions 17-20 on page 4 of the US Department of Justice – Service dogs and the ADA.
A dog that has been admitted may be expelled if it is not under the control of its owner at all times.
Please see questions 27 and 28 on page 6 of the US Department of Justice – Service dogs and the ADA.ADA Service Animals