Per the current CA FTB guidance, property taxes are deductible on your CA state tax return if you itemize and are not subject to the $10k deduction limit that is imposed on the federal return. Local income taxes are not deductible.
https://www.ftb.ca.gov/file/personal/deductions/index.html#Itemized-deductions
https://www.ftb.ca.gov/about-ftb/newsroom/tax-news/march-2019/tax-deduction.html
