Upon a written statement of the president, treasurer or other executive officer having the management of any park or place of amusement located in any county of this State directed to the sheriff of such county, setting forth that in his opinion the interests of the patrons of such park or place of amusement require special police supervision, the sheriff shall appoint as his deputy a discreet and suitable person, satisfactory to the president, treasurer or other executive officer of such park or other place of amusement requesting the appointment and whose salary shall be paid by the park or other place of amusement at the instance of whose president, treasurer or other executive officer the appointment is made, the amount to be fixed by contract with the company owning or operating such park or place of amusement, acting through its president, treasurer or other executive officer.