I know this thread is old, but there is some gross misinformation in here.

First, a dog who is NOT task trained to do something to mitigate the disability is NOT a service animal and does NOT have public access rights, period! If a person has a psychological disability, then an untrained dog may be a ESA and can be on planes and in no pet housing, but that is IT! If you take a dog that is not task trained into public, no pet places, you are breaking federal law!

As to requiring identification....

Federal Law trumps! The ADA states that no vest, ID, etc... is required, therefore states can not require it and can not deny you access if you don't have it.
BUT....should you have an access challenge and decide to take it to court, you may have to prove both that you are disabled and that your dog is properly trained.