On the expiration of terms of members of the first board of directors as set forth in section 247.350, elections shall be held as provided herein and directors elected by the voters of the district for a term of three years. Nominations may be filed with the secretary of the board. The candidates for the board members shall be elected on a nonpartisan ballot. The candidates receiving the most votes shall be elected. Any new member of the board shall qualify in the same manner as the members of the first board qualify.