Hi Heidrun,
the English is correct, but I wonder if changing to:
"Criminal offenses, which are not committed in public should be dealt with anonymously according to this.", would change the meaning in the original.
Well, the original uses the polite "Sie" (like "vous" in French), so it's closer to the original the way it is now. Nevertheless, if it sounds better in passive form, we can change it, of course. It doesn't make a huge difference.
Well, if the request had been "meaning only" I would use the passive form which would sound better in English, but...let's set a poll with the form you chose (perfectly correct), and see. OK?