I have been doing some research on service dog laws (state and federal) and i have not been able to come across any sanctions for lying about having a service dog. With that being said, i can see no down side to telling people he is a service dog so i can bring him places with me as long as there is no penalty for me lying about it.
With that being said, are there any penalties (fines, jail, etc.) that can be imposed if you say your dog is a service dog but really is not?
From 2012....about 16 states have penalties for representing a service dog fraudulently....misdemeanors in most all cases.
This link covers the laws state by state. Hopefully, it helps your research.
Table of State Assistance Animal Laws