Yes, although you will need to apply for residency as a Dependent if you have been coded as Non-Resident by Admissions.
The parent who claims you on their taxes will submit the first page of their tax transcript, or signed Federal 1040, showing that you are claimed as a dependent. We do not need identifying numbers for your parent, so please black these out. We do not need income information for your parent, so this may be blacked out as well.
The parent who lives in Washington will complete the online Residency application and will submit documentation to prove their Washington Residency.
As a dependent, your residency is based on the residency of your parents. If your parents live in separate states, then the state of Washington allows that you could be a resident of either state. It does not matter which state you personally live in. If a parent lives in Washington, you are allowed to claim Washington residency.