"Polizeibericht" usually means a report on e.g. a day's, week's, month's crime statistics.
"Protokoll" is the word you're looking for.

Thanks. Is it just "Protokoll" or "polizeiliches Protokoll" ?

Is it usually possible for a citizen to receive a copy of a Protokoll? If not, is there something else one can request with a summary of the main facts, e.g. in the public domain?

Would it make sense to request the original "Anzeige"? The situation refers to a fine for an "Ordnungswidrigkeit".

Well let me say that LEO is not accurate when it gives "Polizeibericht" as translation for "police report". A police report is generally something the police write up about a specific incident, at least in US English. A general report on crime statistics would probably be referred to as just that: "report on crime statistics."

Now I understand the strange look I got from the police officer when I asked for a copy of the "Polizeibericht." :)

But I still don't understand why you only get an "Aktenzeichen" (AZ) in Germany. You then give this AZ to your insurance company so they can see the Protokoll but you can't?

Does a Protokoll refer only to a statement by one specific person or does it encompass the entire circumstances of a case?

Der polizeiliche Bericht dient in Deutschland auch dazu, gegenüber der Versicherung nachzuweisen, dass zumindest einer der Geschädigten Recht hatte. ...
www.ifa.de/pub/kulturaustausch/.../zfk.../picaper/

Im polizeilichen Bericht zur Blutprobenentnahme sei von den Beamten festgestellt worden, dass die Augen glänzend und die Pupillen stark erweitert gewesen ...
www.jurathek.de/showdocument.php?session...

Heinrich Hannover, Kommunisten im Widerstand
31. Juli 2007 ... Mehr über ihn erfährt man aus einem polizeilichen Bericht, der sich in der Akte findet. Da wird er als »fanatischer Kommunist« bezeichnet, ...
www.sopos.org/aufsaetze/41f7c352795fb/1.phtml