Idaho Code § 31-3705
In cases where the city and county are jointly operating such hospital, and where a hospital or hospitals are being operated by a joint county-city hospital authority, the members of said hospital board or board of trustees shall be appointed by the board of county commissioners and the city council in such manner as may be agreed between them, and where either county or city is alone operating the jointly owned hospital, by the board of county commissioners of the county or the council of the city which is so operating the same. All members of the board shall be subject to removal at any time by the body appointing them, but unless removed shall hold office until the second Monday in the first month of the hospital's fiscal year next following the date of their appointment and until their successors are appointed and qualified; provided, that members of the board of trustees of a joint county-city hospital authority may be removed only for conviction of a felony, mental incapacity, failure to attend meetings of the board as required in the bylaws of the board, or other good and sufficient cause.
The officers of the hospital board shall be a president, secretary and treasurer and such other officers as the board shall designate, all of whom shall be elected by such board. The president must be a member of the board but the secretary and treasurer need not be. It shall be the duty of the secretary of the board to keep an accurate and complete record of all acts and proceedings of the board. It shall be the duty of the treasurer to have custody of all funds coming into the custody of the board and he shall perform such other duties as are herein specified, and he shall give bond in such amount as shall be fixed by the board in the same manner and on the same terms and conditions as required for the official bonds of county officers. All officers of the hospital board shall be subject to removal by said board at any time. The hospital board and any of its officers or members may be paid reasonable compensation as shall be authorized by the board and/or council authorized to appoint the members of the board.
Meetings of the hospital board shall be held at such time and place and under such rules and regulations as the board may establish. A majority of the board shall constitute a quorum for the transaction of business, and a majority vote of the members present at any meeting properly called shall govern as to all questions coming before the meeting.
Idaho Code § 31-3705