California uses the "honor system" to vet their voters, very little else: same day registration, no voter ID requirements, etc.
I registered to vote in WA state, and no one asked to see my US Citizenship by Naturalization certificate. It was and is strictly an honor system. Before that I registered in Illinois, and IIRC it was a democrat precinct captain who came to my home and registered me. Again, did not ask to see proof of citizenship.