It depends. Some states grant automatic extensions with the filing of the federal extension. Other states require separate extensions.
Check with your state. You can find links to state tax websites at How do I track my state refund?
The link does not go the the California Tax website, it just moves through the Intuit website, so this did not answer the question regarding automatically filing a CA state extension.
State of California Franchise Tax Board: Extension to file
IRS State Government Websites