The IRS will not be monitoring the state withholdings, only the federal, so they will not be involved in the move from California to Washington.
You are correct, there is not individual state income tax in Washington, so you will not need to file a resident return there.
First, please check My Info in the Federal return and be sure the box is checked for Made money in another state and that your address is listed as the correct address in Washington.
Then, in the California return, be sure it is listed as a Non-Resident return and on the income allocation screen, you will enter California income as 0. This should prompt the return of the withholding that took place at the beginning of the year.
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