Police vehicles through history.

New York mayor Fiorello LaGuardia (back seat, right) takes a spin
in a New York World's Fair police car, ca. 1939–40. NYPL.

Tokyo's Police Museum has just opened a "history of police vehicles" exhibition, but those not in Japan can view modes of transportation for law enforcement in other places:

• Baltimore City Police Motors Unit
• Police vehicles, Carbondale (IL) Police Department
• Massachusetts State Police horseback patrols, 1920s–1930s 
• Metropolitan policewomen on motorcycles, London, 1920
• Metropolitan Police car and motorcycle, London, ca. 1935
• Vehicles gallery, National Border Patrol Museum
• Ohio State Highway patrol vehicles
• Police car retrospective
• Restoration of a 1972 Plymouth Fury patrol car, Pennsylvania State Police
• Portland Police Mounted Patrol, Portland (OR) Police Museum 
• Historic fleet, San Diego Police Museum
• Vintage police cars, Seattle Metropolitan Police Museum 
• Patrol wagon-ambulance, Trenton (NJ) Police Museum, ca. 1910
• Police jeeps, US Air Force police, 1950s