The following vehicles shall be exempt from registration:

(1)  Motor-propelled fire engines and other fire apparatus. However, the division of motor vehicles shall issue a permanent registration plate and certificate for each motor-propelled fire engine or fire apparatus for its life at no fee;

(2)  Every motor vehicle which is propelled by electric power obtained from overhead trolley wires but not operated upon rails.

(3)  Motor-propelled vehicles employed for law enforcement purposes by the several city and town police departments whether or not equipped with distinctive registration plates. A permanent registration plate and certificate shall, however, be issued for each motor-propelled police vehicle, for its life, at no fee. However, any existing police vehicle plate currently on a propelled police vehicle will pay a five dollar ($5.00) transfer fee if that plate is transferred to another police vehicle within the same police department.