Of course not. You aren't a citizen. So if you try to vote in a US election you will be caught and put on trial.
But the processes for handling transactions, enforcing laws, etc are all mostly the same for citizens and non-citizens, especially at state level laws. If you get arrested and put on trial you will be treated the same up to a certain point.
Most any local laws will want to make your stay as pleasant as possible to get tourism dollars. So police may overlook minor stuff. Just don't push your luck. Police will also freak out whenever they see something outside of normal American behavior.
If get pulled over while driving stay in your car. It may be acceptable to get out and visit with the police in other countries, but in the US the police will quickly aim their guns at you assuming you are about to attack.