First off, a bit of background on "Du" vs. "Sie".
"Du" is an informal address usually reserved to family and friends. There are special groups where group membership pretty much implies using "Du" (like when you're part of a sports team -- it would be strange to use formal address in those environments). Certain workplace environments encourage "Du", others don't.
Saying "Du" where a "Sie" would be expected -- like when addressing your company's CEO, a police officer, or your doctor -- would be considered uncourtly. Much depends on the exact circumstances. A drunk person, someone mentally challenged, a non-native speaker etc. can easily get away with calling everyone "du". There is nothing inherently insulting in saying "Du", it's just not appropriate everywhere. More like a faux-pas. However, depending on context, it can give the impression of you being insulting.
Someone who is arguing about a speeding ticket in a raised voice and insisting on saying "du" to a police officer is meaning to be disrespectful. And this is where the difference is being made -- not so much in which word you use, but how you use it.
(The English equivalent "other" pronoun -- "thou" -- has fallen out of favor. It also was much less clear when it was meant to express familiarity with a person or disdain.)
Now we're entering legal territory, so first off, I am not a lawyer and this is not legal counseling.
In Germany, insulting someone can be prosecuted. The relevant law is § 185 StGB (StGB being the German penal code). Punishment can be a fine or even jail time.
Fines in Germany are generally issued as day-fines, i.e. there is no fixed amount but rather the fine is made to fit that person's income. So the line "up to 600 Euro" is doubtful, especially since the law does allow for the judge to decide on jail time, so there's nothing "up to" with 600 quid when severe cases can earn you a year behind bars.
This is true for everybody, not just police officers. Surprisingly enough, although there is even a word for it ("Beamtenbeleidigung"), there is no special law against insulting a police officer (there is § 188 StGB but that is not applicable here as it refers to insulting someone in public office in a larger scope, e.g. by disseminating insulting content).
Again, saying "Du" to a police officer, while definitely inappropriate, is not an insult in itself, especially not when coming from a non-native speaker. You can readily insult someone calling them "Sie" as well. "Du" and "Sie" don't make much of a difference, when the next word is "a**hole".
: Note that omitting a "Sie" is often, effectively, the same as saying "du":
"Geben Sie bitte mal her." -- "Gib bitte mal her."
Either is a polite request, but the latter is to a person you're acquainted with, whereas the former could be to a total stranger. Neither would be impolite. Saying the former to a friend would be just as "off" as saying the latter to a stranger in a formal environment.
"Geben Sie her!" -- "Gib her!"
Both are a command, again the latter being the equivalent of "duzen", and again either one being completely "off" if used in the wrong context, but not in fact being insulting. Not saying "please", and not framing it as a request, but still not an insult per se.
Calling someone names however doesn't get any less insulting by saying "Sie".