Washington does not require that attorneys carry professional liability insurance. However, as of this writing, a move is afoot within the Washington Bar Association to change this and require all Washington lawyers to maintain such insurance.
Presently, the public can confirm whether or not any Washington-licensed lawyer has such insurance on the Washington Bar Association's website. However, the amount of insurance coverage is not available to the public. It can be obtained, along with a copy of the policy itself, by the plaintiff after a lawsuit has been commenced, through the "discovery" rules. Often that information is shared between counsel upon request before a lawsuit is filed, in order to facilitate settlement discussions, but the would-be defendant is not required to divulge the information pre-suit.
In this firm's experience, Washington lawyers who do carry professional liability insurance usually have coverage in the amount of $500,000 or greater.
Oregon, on the other hand, requires that all licensed attorneys maintain professional liability insurance, with a minimum coverage of $300,000. Painfully often, many sole practitioner attorneys and small firms do not supplement this insurance with more coverage. Larger firms typically care significantly more, as do many smaller firms as well.