The answer is yes if your rental is in Berkeley, E. Palo Alto, Hayward, Los Angeles, San Francisco, Santa Cruz, Santa Monica, Watsonville (Watsonville?), and West Holllywood. In Santa Monica and E. Palo Alto you must keep the funds separate in and FDIC type of account. You must pay once a year and the end of the tenancy.
The interest rates vary greatly. You must call each city to find out the rate there. I checked Los Angeles City. The rate for 2015 is .12%. What does this mean in the real world? If a tenant’s security deposit is $3,000.00, the interest for next year would be $3.60 unless my calculator is acting up. So much ado about nothing.
Providers of Housing to the Public (I do not like the word Landlord), one thing I used to say to a prospective tenant when trying to close was, “I will pay you interest on your deposit” even though the property was not in one of the above cities. It was a lot cheaper than giving a free month’s rent.