From the instructions to California Schedule S:

*A dual resident is any taxpayer who is defined as a California resident under California law and a Virginia resident under Virginia law. If you are a dual resident, you are allowed to claim the other state tax credit for taxes paid to Virginia on Virginia source income.

Then it adds the following, because many members of Congress "live" in Virginia while representing their state or district back home:

Dual residents who are elected or appointed officials and staff as defined in R&TC Section 17014(b) may claim the other state tax credit for taxes paid to Virginia on all income taxed by Virginia whether or not it has a source in Virginia.

I would file resident returns for both states, if the 183-day test in Virginia is met, and take credit for California tax on the Virginia return.