(a) The governing body of each county may establish, and appropriate an amount to support, a county public library system free from political influence.

(b) Each county public library system shall be governed by a board of trustees. However, a charter county may:

(1) Establish a county library agency and grant it some or all of the powers of a board of trustees; or

(2) Have a board of library trustees, provide for the board’s selection, and determine its powers.