Do I have to pay taxes on my inheritance in California?

On any money or property you inherit there is no federal tax. Also CA does not have inheritance tax.

For more information read: Your U.S. Tax Return: Tax on Inheritances

Any taxes due on an inheritance is paid by the estate before distribution of the inheritance. However, if the inheritance included property or non cash assets, you may owe tax on your profit from the liquidation of the assets. The property should be valued as of the date of death. That becomes your cost basis. Any difference in the amount the property was sold for can be either profit or loss.