Oregon Revised Statutes Public Officers and Employees § 236.225

(1) If vacancies exist at the same time in all of the offices of members of a county governing body, two qualified persons shall be appointed by the Governor, and one by the appointees of the Governor, to perform the duties of the offices until the vacancies are filled as provided by law. If vacancies exist at the same time in all but one of such offices, the Governor shall appoint one qualified person who, with the incumbent serving in office, shall appoint another, each to perform the duties of the offices until the vacancies are filled. If county judge is one of the offices vacant, one of the appointments made by the Governor under this section shall be to the office of county judge.

(2) When a county charter establishes a county governing body with more than three members, if a number of vacancies exist at the same time in the offices of members of that governing body so that all the remaining members do not constitute a quorum for the conduct of county business, the Governor shall appoint to the vacant offices the minimum number of qualified persons sufficient, with the incumbent members of the county governing body, to form a quorum. Persons appointed by the Governor under this subsection, together with the incumbent members serving in office, shall appoint qualified persons to the remaining vacant offices. All persons appointed under this subsection shall perform the duties of the office of member of the county governing body until the vacancies are filled as provided by law.

(3) ORS 236.100 applies to appointments under this section.