I will move to and work in CA in 2020. I will have interest income (but no earned income) from a savings account based in NC in 2020. Do I have to file in NC or only CA?

[TomD8]

If you move out of NC in 2020, you will have to file a 2020 NC part-year resident return only if your NC-source income exceeds the NC filing threshold for your filing status.  For the details about that, see the "part-year resident" section of this web reference:  https://www.ncdor.gov/taxes-forms/individual-income-tax/individual-income-filing-requirements

Interest income earned as an NC resident is NC-source income.

[Hal_Al]

The interest you received while an NC resident will be taxable by NC. The interest you received while a CA resident will be taxable by CA.