In Washington state, you generally have three years to file your personal injury lawsuit after the date of the accident. Your lawyer will tell you whether to file sooner than the statute of limitations’ three-year deadline, but as long as you get those papers filed before the three-year mark, you're in good shape.
While there’s no statute of limitations for filing an insurance claim after an accident, most insurance companies want you to file promptly or within a reasonable timeframe. Make sure you check with your insurance company to find out their requirements.
Take note that claims against the federal government or government agencies have shorter statutes of limitation and litigation claim filing requirements. Always see an attorney as soon after an accident as possible, to determine the appropriate claim filing requirement and claim notice requirements.