When we change the structure of an interrogative sentence, such as:
Am I not supposed to go there?
like this:
I'm not supposed to go there?
Does the meaning stay the same? If not, are there any cases it might make a difference?
In general, I think you can consider the two to have pretty much the same meaning. Depending on the context, there might be slight differences in nuance, but they would generally be pretty small.
The first form ("Am I not supposed to go there?") is a bit more formal, and thus might be more likely to be said when somebody is trying to be polite or respectful. In some contexts it might also be chosen if one wanted to be particularly dramatic or even condescending (if said in a particular tone of voice, etc).
The second form ("I'm not supposed to go there?") is slightly more informal, and does also come across as a little more abrupt, and thus could indicate a somewhat greater degree of surprise on the part of the speaker (i.e. implying something along the lines of "I always thought that was ok, but now you're telling me I'm not supposed to go there?")
Depending on the tone of voice, etc, the second form could also express some amount of disbelief ("Oh really? I'm not supposed to go there? Are you sure about that?")
All of these distinctions, as I mentioned, are pretty subtle, though. In many cases you could do the same thing using the other phrase too. This is all really approaching the level of splitting hairs and personal opinions to some degree...