Personal Tax Information: 

The State of Washington has no state income tax, so no need to file anything else if you were approved for your federal tax extension.

For more information, visit the State of Washington Department of Revenue.
http://dor.wa.gov/Content/Home/Default.aspx

Business Tax Information:

The State of Washington does not have a state income tax. Therefore, there is no state of Washington business income tax extension. If you received a confirmation email from ExpressExtension that your federal tax extension was approved, there’s nothing more you need to do.

For additional information, including other taxes that may apply to your business, please visit the State of Washington Department of Revenue.
http://dor.wa.gov/Content/Home/Default.aspx