Washington does not have a personal income tax. On the screen that asks you if you made money in any other states, just above the list of states it says "Leave No Entry if if you only received income in Alaska, Nevada, South Dakota, Texas, Washington, or Wyoming. You don't pay income tax in these states."

Do what it says. Leave it set to "No entry." Do not select a state from the list. Just click Continue at the bottom of the page.