Within 30 days of the receipt by the district governing board of the employee’s demand for a hearing, the employee and the governing board shall agree upon an arbitrator to hear the matter. When there is agreement as to the arbitrator, the employee and the governing board shall enter into the records of the governing board written confirmation of the agreement signed by the employee and an authorized representative of the governing board. Upon entry of such confirmation, the arbitrator shall assume complete and sole jurisdiction over the matter.