I don't practice in Seattle, and I haven't researched this, so take my answer with a grain of salt. I am answering simply because your question has been up for a while and you don't have an answer yet.
I am not aware of any Washington State law or City of Seattle Municipal Code requirement that a person wear a helmet while on a Segway. I think the law considers a Segway to be an "Electric personal assistive mobility device" or EPAMD. There are a number of laws that relate to the usage of these. In Seattle, since that looks like where you are, it looks like SMC 11.46 would be your guide, while state law would fall under RCW 46.61 and 46.04. Both local and State law would apply. I'd be happy if someone else chimed in, but it doesn't appear a helmet is required.
Again, I didn't research this, I just took a quick look and could easily have missed something. This is not legal advice that is ok to not wear a helmet. You should take a more careful look for yourself to be certain, or if you really want certainty, you could hire one of the many good attorneys in your area to look into it and provide a more solid answer (probably not very cost effective for you).