A similar threat was sent me and i let google know ASAP. They assured me that they will continue to monitor my account for few days for any illegal activities. So, you should let Google know (send them the copy of th threat), at least they will know it wasn't you.
just inform google. install ad logger and keep monitor your income or suspicious click fraud. report google immediately if got any suspicious increase no. of clicks. i think google will understand. there are many a$$ like that on the internet. you can not do anything to them but make sure you know how to protect yourself.