The idiom mainly comes from magic shows, where the magician would, prior to doing some slight of hand trick, say "There's nothing up my sleeves" and push up the floppy sleeves of his jacket to show that nothing was hidden there. (The idiom also references, of course, the practice of hiding cards up ones sleeves when cheating at cards. It's probably impossible to assign the origin of the idiom to one scenario or the other.)
Of course, magician's action was very likely a distraction (in a fashion typical of prestidigitators) while he in fact hid something up his sleeve or otherwise set up the trick, but such deceit is not implied by the idiom, which, in its simplest interpretation, means "I'm not hiding anything".
The idiom may also be used (with a slightly different meaning) in, say, a business discussion, where a problem is being discussed, and one party asks another if he has anything up his sleeve to address the issue. In this case, the question is asking whether the second party has any useful ideas or information which he may not have thought to mention. (The question is not used in an accusative sense, but rather to promote open discussion.)
It's unclear what the context is in the original question, but if someone tells a cop or (more likely) a prosecutor that he (the cop/prosecutor) has nothing up his sleeves then the intended meaning may be more like the business sense, and the speaker may be saying that the cop/prosecutor has no case and no hidden information he can use to make a case.