I live in Los Angeles and we are required to register our dogs with the City/County. If we are caught with them in public without registration we can be fined. Though I have registered Bella, I can't recall a situation where I was ever asked for the registration tags; however, there is another thread on YT that's currently hot where someone got a ticket because they didn't have their dog's registration tags on them. Bella's registration was only $10.00 (or around that ballpark), better safe then sorry I say. You should be able to get information on registration at your local animal shelter.
Here are the links for CA's pet licensing information:
http://animalcontrol.co.la.ca.us/html/Main1.htm http://www.ci.la.ca.us/ANI/doglicense.htm