If you are the spouse of a nonresident service member stationed in California, income you earn here can be exempt from California income tax. You can choose to claim your service member spouse’s state of residence, your own state of residence, or the state where their permanent duty station is, for tax purposes.
There is nothing to file with a state office in advance. Claim the exemption when you file, and give your employer your residency election so California tax is not withheld.
Your service member spouse’s orders assigning them to California, proof that you both are residents of another state, and your marriage certificate.