@Jan.Sraml: The correct word order in your first sentence is "Melden Sie mir das nicht." (If only one of the objects is a pronoun, then this one comes first).
"Do not report to me" would rather be understood as "Melden Sie es mir nicht". In English you can leave out those kind of impersonal objects, but in German you can't.
I'm not good enough in English to know how to translate "Melden Sie sich nicht bei mir" ("bei has to stand here), especially not if this could be a possible meaning of "Do not report to me" as well.
In the context of the preceding question about a pupil "melding :) sich" in a class, I have pictured a person saying this sentence in the sense of "Do not raise my hand for me!" Is this totally impossible? Or how can this person use "melden" (with or without any prefix) to protest like this?
So, without the "flavours", would it be "Melden Sie mir das nicht."? Or "das mir"?
Melden Sie mir das nicht! (Don't report that to me!) or Melden Sie das nicht mir! (Don't report that to ME [but rather to someone else]!) are possible.
Melden Sie das mir nicht! is not -- the personal pronoun mir comes before das.
And "Do not report to me" would be "Melden Sie sich nicht mir."? Or "bei mir"?
And what if "report to me" is used not in the sense of reporting oneself to me, but of being subordinate to me?
I'm not sure whether such a command makes sense -- people don't pick who they are subordinate to, usually; they get told. That's kind of the point of being subordinate, after all: you follow instructions.
Thanks for the answer. To me, such an exhortation makes sense. E.g. when someone tends to behave as if you were their boss, and you need to make it clear that you are not. Or if you are redirecting the person in the chain of command. (In outsourcing, especially if the person will work with the client's confidential data; in army, lending a specialist to regular units.) Only, perhaps, one would say that in English in some other way.