rxter, the Trabant was actually made in Germany (east). They had a 2-stroke engine. Mix your own fuel out of heating oil stock (something like 50 parts oil, one part gasoline). The outer body pieces were made of plastic. Noisy, smoky, and plain by western standards, but cheap to own and maintain and thus very practical.
I doubt they were used by Russian police. In Moskow they have all kinds, Mercedes, BMW, Land Rover -- and apparently at least one Porsche? In small towns usually older Lada and Niva (Russian Jeep). Police is very important social position and comes with company car!
Jack