Every official bond executed by any officer pursuant to law is in force and obligatory upon the principal and sureties therein for:
(a) Any and all breaches of the conditions thereof committed during the time such officer continues to discharge any of the duties of or hold the office, and whether such breaches are committed or suffered by the principal officer, his deputy, or clerk except that no officer of a county, city, or city and county, whose sole compensation by virtue of his office is a fixed salary established by the Legislature, the local governing body, or the board of supervisors, shall be personally liable for the negligent act or omission of any deputy or employee serving under him and performing the duties of his office, where the appointment or qualification of such deputy or employee is required to be and has been approved by the local governing body or the board of supervisors, or by the civil service commission, unless the officer failed to exercise due care in the selection appointment or supervision of such deputy or employee, or negligently failed to suspend or secure the discharge of such deputy or employee after knowledge or notice of his inefficiency or incompetency, and except that no state officer shall be personally liable for the negligent act or omission of any deputy or employee serving under him and performing the duties of his office, where the appointment or qualification of such deputy or employee is required to be and has been approved by the State Personnel Board, unless such officer failed to exercise due care in the selection, appointment, or supervision of such deputy or employee, or negligently failed to suspend or secure the discharge of such deputy or employee after knowledge or notice of his inefficiency or incompetency. Nothing in this section shall be interpreted as placing any liability upon the principal officer for the act of a deputy or employee unless such liability is otherwise imposed upon the principal officer by law, nor shall this section be construed or interpreted as releasing or relieving any such county, city, or city and county of any liability for the negligent act or omission of any such deputy or employee otherwise imposed by law.