I can confirm that either party may request a machine recount if the difference is more than 2000, but they must put a deposit, and pay for, the cost of the recount.
I am not sure about a hand recount and will check.
A hand recount costs 25 cents per vote, as opposed to 15 cents for a machine recount.
http://www.secstate.wa.gov/office/osos_news.aspx?i=SPlmpeBt1xLxpksVqw%2ft9w%3d%3d