Duden defines the primary meaning as "Strafanzeige erstatten", and "Strafanzeige" as "Mitteilung einer Straftat an die Polizei oder Staatsanwaltschaft".
Basically, you are reporting a crime to an authority which has the authority to prosecute that crime.
So the recipient of such an "Anzeige, Strafanzeige" has to be someone with such authority to prosecute crime: for normal people, that's always the police.
You can report a lazy co-worker to your boss, but you can't "beim Chef Anzeige gegen den Mitarbeiter erstatten" or "den Mitarbeiter beim Chef anzeigen", not only because laziness is not a crime but also because your boss has no authority to prosecute it even if it were one (say, stealing).
Well, normally you would only report someone to the police who has committed a crime; if there is anything sinister in the act, it's the crime, not the reporting. I suppose you could call it outing or snitching for telling the police that you saw a burglar climb into your house.
But the term anzeigen itself is neutral.
You can use it for a burglar, or for your friend who did some insider trading that "didn't harm anyone".