Trust Administration: Does a Living Trust Have to be Filed With the Pobate Court

When a person has a will and a revocable trust dies, I know that a copy of the will has to be filed with, I think, the county clerk. But is the trustee required to file a copy of the trust with the county also?
This is in the state of Washington.

Thank you.

Trust Administration: Does a Living Trust Have to be Filed With the Pobate Court