Each board of library trustees appointed pursuant to sections 3375.06, 3375.10, 3375.12, 3375.15, 3375.22, and 3375.30 of the Revised Code shall meet not later than January of each year and may meet in December of the preceding year and organize by selecting from its membership a president, a vice-president, and a secretary who shall serve for a term of one year commencing the later of the first day of January or the date of selection. At the same meeting, each board shall elect and fix the compensation of a fiscal officer, who may be a member of the board, and who shall serve for a term of one year commencing the later of the first day of January or the date of election. Except as otherwise provided in section 3.061 of the Revised Code, the fiscal officer, before entering upon official duties, shall execute a bond in an amount and with surety to be approved by the board, payable to the board, and conditioned for the faithful performance of the official duties required of the fiscal officer.