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I grew up hunting squirrels in Kentucky. They taste great, especially with gravy and a biscuit. However, grandma said it was bad luck to shoot one in the yard. You've been warned.
Here's another page from the WDFW with more scoop on squirrels, including the legal status of the various species: http://wdfw.wa.gov/living/tree_squirrels.html
One thing to hold in mind is that they can carry plague, something that I believe is endemic to this part of the country.