No employee of a public library shall be discharged or removed from office except by the library trustees for malfeasance, misfeasance, or inefficiency in office, or incapacity or unfitness to perform the employee’s duties. Prior to the discharge or removal of any such employee, a statement of the grounds and reasons therefor shall be prepared by the library trustees, and signed by a majority of the board, and notice thereof shall be given to the employee not less than 15 days nor more than 30 days prior to the effective date of such discharge or removal. Upon receipt of said notice and within 30 days thereafter, but not otherwise, the employee may request a public hearing. If such request is made, the library trustees shall hold a public hearing on such discharge or removal. The hearing shall be held not more than 30 days after receipt of the request for the hearing, and if the trustees, upon due hearing, shall find good cause for discharge or removal of the employee, they shall order the employee’s discharge or removal from office. There shall be no change in salary of such employee during the proceedings for discharge or removal nor until the final effective date of the order for discharge or removal. The provisions of this section shall apply to the employees of any public library except in a case where the city or town has personnel rules and regulations which apply to such employees and which make provision for a public hearing in the case of such discharge or removal.