Thank you for your replies! I believe I need to file a Form 540NR (California Nonresident). However, I'm not sure how to start filing this out in TurboTax (I downloaded the California State return file already).
Here is what the employer said:
As someone who moved from a U.S. state to another state between 2019 and 2023*, you may be required to file multiple U.S. state tax returns by 15 April 2024 (filing extensions may be available). Your [RSU] income is included in your Form W-2 together with your other employment income (e.g. base pay, bonus, etc.). Check your statement for your equity income allocation between locations.
If the [RSU] awards that were granted to you while you were a resident of another state vested in 2023 after your location transfer, [employer] reported your [RSU] income and withheld corresponding taxes in both states based on the state requirements. Depending on your situation, you may need to file U.S. state tax return(s) for the previous and current U.S. states (in addition to your Federal tax return) to report your equity income on your annual income tax return. Your final tax liability is determined through your tax return.
