Translation:I have nothing to do with that case.
Do remember that specific use of which prepositions is one the things that varies very greatly between languages.. and therefore represents one of the steepest stumbling blocks when translating. What is very much "in" to you, may so obviously be "on" to the speaker of another language. :-)
DL may have been avoiding the more general English expression "in that/this case" meaning, "under those/these circumstances", or "in that/this situation", and usually translated in French as "dans ce cas".
"Case" is actually kind of a tricky word to use in translation, because it absolutely can mean a legal undertaking (or a police investigation), but it does often carry that more general meaning.
"I have nothing to do with the case" might carry the "legal" meaning, but could very easily mean, "I am not personally involved in what we've been discussing." Context would tell all.
In English, I have nothing to do with the/this/that case means you are not connected with it in any way.
In English, I have nothing to do in this case can mean you do have something to do with it but have nothing to do in it. It may very well be a complaint that you are being prevented from actually getting something to do in the case that you are connected to. You are assigned some degree of responsibility but are being left out of the loop.
What I don't understand is why I have nothing to do in the/this case is accepted but that case is not.
What does rien à faire really (and literally) mean? The hints aren't being very hinting.
Prepositions are some of the trickiest things in dealing with foreign languages. Although the speaker may have one meaning in mind when saying in this case it is not at all necessarily clear what saying that actually means.
Do you mean you mean someone in the case has nothing to do? Or do you mean someone who has lots to do has nothing connected to the case? Of do you mean in this case (in this event) now that you have taken my keys away I have nothing to do? What might be evident in one language is not so clear in another language where the same preposition is used differently.