If I won a jackpot at a California Casino and had no other earnings in California do I have to file State taxes?

I assume you are not a CA resident, corect?

If you have CA source income (i.e. casino winnings) and if your total income from all sources exceeds the filing threshold then yes, you are supposed to file a non-resident return with CA. The income threshold that requires filing depends on your filing status (single versus married) and number of dependents you have - see the following web page for details: https://www.ftb.ca.gov/forms/2012_California_Tax_Rates_and_Exemptions.shtml#ifr - go to the section titled "Individual Filing Requirements" near the bottom of the page.