Sorry about the delayed reply - I just saw this comment. Missed it when I posted earlier.
Anyhow, there are already regs in Los Angeles that require anyone who posts a "no parking" sign post the code for the type of parking that's being enforced and the information for who to call if your car gets towed (either 3-1-1 or a local station). City signs may say they're from the city and also say "impounded" instead of "towed". Grouped city signs (like you see for street sweeping) aren't required to all bear contact info, but some must. If there's no police contact number on a stand alone sign, it's not really a city sign.
Even a correctly placed sign for private property (like the ones in our alley to prevent people from blocking our cars in our garages) has to list the number for the private tow company that will be called if your car vanishes. If there's no number, and no code, it's not an official, enforceable private sign. Anyone towing on a sign missing that information will be fined themselves AND have to pay for your tow.