In this scenario, do the taxes that Californians now pay to DC then go to Sacramento instead?
Although I believe secession to be unconstitutional, I'll play along on this thought exercise.
Regarding the law, if California secedes, naturally all federal laws will cease to apply. That means no Bill of Rights, no social security, no veterans administration, no treaty enforcement, etc. California will have to start fresh with applying to the United Nations, signing the Geneva Convention accords, and other international agreements that cover travel safe harbor, extradition, financial transfers, trade, etc. One has to assume that none of these things signed by the United States descends to an independent California.
Regarding state law, would the California state constitution still be valid, as California is no longer a state? Many laws were written to coexist within the federal framework that no longer applies; there may be huge gaps in the applicability of the existing set of laws. Also, if existing state law becomes nullified too, there will be a period of chaos while new government is formed, new laws are passed, etc.
I don't think things can legally be the same, just independently.
-PJ