tl;dr - no
A landowner had both legal rights and responsibilities (such as paying taxes) so ownership needs to be tracked by the state and is a pubic record. A tenant; however, has no public responsibility. His responsibility is to the owner. This certainly can vary by state; but, I have never heard of any responsibility to register a property's tenant - only its owner.
Someone might be able to infer tenancy from a person's current address; but, registering your address does not necessarily mean you pay the rent. "Everything is on the internet"; so, I wouldn't be surprised if someone figured out a way to determine it (like from instance from utility bills); but, I doubt you'll find it on a state registry.
I skimmed the Washington Rental Laws and I didn't see anything.