yea most squirrels are legal to shot in this state just a few that are protected there is a page on wdfw to tell you which squirrels you cant shoot. california aka grave diggers are invasive to wa and are great fun to take care of for ranchers and orchards.
The Western gray squirrel is classified as a threatened species and cannot be hunted, trapped, or killed (WAC 232-12-007). The red squirrel, Douglas squirrel, and Northern flying squirrel are protected species and can be trapped or killed only in emergency situations when they are damaging crops or domestic animals (RCW 77.36.030). A special permit is required in such situations.
The Eastern gray squirrel and Eastern fox squirrel are unclassified and may be trapped or killed year-round as long as you have a hunting license. In such cases, no special trapping permit is necessary for the use of live traps. However, a special trapping permit is required for the use of all traps other than live traps (RCW 77.15.192, 77.15.194; WAC 232-12-142).