I looked it up and this is what you need to start service.
To start service, you’ll need:
- Service address
- New service start date
- Identification: Social Security Number (last four digits), Driver’s License or State Identification
customers such as multi-family units and businesses can call Customer Service at 1-866-403-2683, Monday-Friday (8 a.m. - 4:30 p.m.)
There's no requirement there for you to produce a lease or any other sort of paperwork regarding authorization to occupy the property. Most of the time, clerks and city personnel are way too busy to dig into anything regarding leasing etc, so as long as you pretend you're using the property for its zoned purpose, as long as you pay the bill on time they aren't likely to come looking for you.
Someone else may have more expertise in this area as I have no direct knowledge of how CA authorities behave. I just know that most places don't really care what you're doing as long as you're clean, quiet, and pay the bills.