No - the California Franchise Tax Board does not need to be notified that your federal return has been extended on Form 4868 - you just need to file your California return by October 16th, the extended due date. The FTB allows automatic extension of the California return, with no state extension needed, if a refund is anticipated, or no tax due. However, if a payment needs to be made, it should be made online or by credit card on the FTB website, or via check together with Form FTB-3519, by April 18th, to avoid any penalties or interest.
Please see California FTB FAQ, "How Can I Get an Extension to File?"
https://www.ftb.ca.gov/individuals/faq/ivr/201.shtml
