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 isn't in the drop down menu of Box 15 of form 1099-INT. Just leave boxes 15 and 16 blank even if WA is listed in box 15 and box 16 is filled with an amount on your form 1099-INT.