I moved to a state that does not have state income tax, but my employer kept withholding for my old state. Can I get that money refunded?

[swirleigh]

I lived and worked in California until Dec  2019, then lived and worked in Washington State 1/1/20.

[SweetieJean]

Did you work at home in WA for that same CA-based employer?  Did you ever visit CA on business for that employer?

[swirleigh]

The employer's office was actually in Chicago. I worked remotely from home in California in 2019, then Washington all of 2020.

[DanielV01]

Yes you can, but it will require a state tax return.  If you were having taxes withheld to California, then you will file a California return with $0 income (if you resided in WA all of 2020).  If your employer withheld Illinois (not likely, but possible), then you file an Illinois tax return with $0 income.  Any taxes withheld will be refunded.  

Keep in mind that either of these states could ask for proof that you don't live there and were not working there.