Moved from WA to CA for work. Do I need to change residency?

I recently graduated from school in WA, got offered a job back home (CA), and moved to CA 2 months ago.

I did not work in WA at all.

Do I need to change my drivers license and everything to establish CA residency for tax purposes?

I put my CA address on my job documents but everything else is WA (car license plate, drivers license plate, etc.)