Hospital trustees shall qualify by taking the usual oath of office as provided in chapter 63 and organize by the election of a chairperson, a secretary, and a treasurer. The secretary shall report to the county auditor and county treasurer the names of the chairperson, secretary, and treasurer of the board of hospital trustees as soon as practicable after the qualification of each. A board of hospital trustees shall meet as necessary to adequately oversee the operation of the hospital. A majority of the board of trustees shall constitute a quorum necessary for actions by the board of hospital trustees. The secretary shall maintain a complete record of board meetings, proceedings, and actions.