Nine states — Alaska, Florida, Nevada, New Hampshire, South Dakota, Tennessee, Texas, Washington and Wyoming — have no state income taxes.
As your state, Washington has no state income tax, it is not in the drop down menu of Box 13 of form W-2G. Just leave boxes 14 and 16 blank even if WA is listed in box 13 and box 16 is filled with an amount on your form W-2G.