Yes. Whether you were injured by a negligent driver or because of dangerous sidewalk hazards, these are personal injury claims. Seattle property owners, including the state, might be obligated to provide specific legal duties to bike riders. These duties may include inspecting and making designated bike areas reasonably safe for riders, or warning riders of potential roadway hazards.
Special procedural rules apply to negligence claims against a state or local government. You might need an accident lawyer to help you file an administrative claim with your local transportation department for injuries caused by a roadway or sidewalk hazard.