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The short answer generally is yes. However, the resource I have linked to is an excellent primer on CA landlord tenant relations and should answer all your questions. It also has a link to information regarding the small claim process in CA. If you want to confirm with a CA lawyer the status of your legal rights you can look one up here on Avvo (some of whom give free consultations) or contact your local lawyer referral service.
I would agree with the answer provided by the moderator, with one additional note. If you are on a month-to-month rental agreement, you might be able to avoid paying part of the rent by giving your landlord prompt 30-day notice terminating your rental agreement. That is, upon receiving the 60 day notice, send your landlord a notice that you intend to vacate the apartment and end your tenancy the following month.
Such a notice only becomes effective the month following the month in which you give notice - that is, if you send notice to your landlord on May 2nd, you are obligated to pay your rent for both May and the following month, June, since your 30 day notice is too late to be effective for May, and would only become effective beginning June 1st. If, however, you gave notice on May 29th, you would only have to pay rent for June since your 30 day notice would become effective the first day of the next month, June 1st.
So, if you received the 60 day notice near the end of one month, say May 29th, requiring you to vacate at the end of July (60 days later), you could immediately give written notice of intent to vacate at the end of June and avoid having to pay the July rent.