All new vehicles, otherwise taxable under §§ 249-1 to 249-13, in stock for purposes of sale, shall be exempt from the tax herein provided, and number plates for all these vehicles may be issued as now and hereafter provided by ordinance of the county. All motor vehicles owned or leased for twelve months or longer by the State or any county and all motor vehicles and motorcycles owned or leased for twelve months or longer by police officers of the State or any county that actually are used by them in their travel on official business shall be exempt from the tax herein provided, and number plates for all these vehicles may be issued as provided by ordinance of the county; provided that the director of finance may charge the State an amount equal to the cost to the county of the number plates issued to the State.