The Commissioner of Agriculture may, upon the application of the Oystermen’s Protective Association of Connecticut or the owner of any oyster franchise or grounds or any natural growers’ association, during such time as the commissioner may determine, appoint and commission such number of policemen as he deems necessary to be designated by such association or owner, who, having been sworn to the faithful performance of their duties, may act as policemen upon the tidal waters and flats of this state and upon any boats, wharves or docks owned, leased or controlled by said association or a member thereof or an owner of oyster grounds. Said commissioner shall cause a record to be made of the issuance or revocation of any such commission. Any person so appointed shall have the powers to make arrests and, when on duty, shall wear in plain view a badge bearing conspicuously the words “Shellfish Policeman”.