Health Care Authority PO Box 45510 Olympia, WA 98504-5510. Certified and FedEx mail: The sender cannot send this type of mail to a post office box. Refer to the USPS or FedEx mailing forms for their specific format. Office of Hospital Finance Health Care Authority (optional) Cherry Street Plaza 5th Floor (MS:45510) 626 8th Avenue SE Olympia, WA ....