You've gotten some awesome responses already. But just to chip in...
We're planning an apartment HB too. We are in one of 4 apartments in a big old farmhouse build in the 19th century. The walls are a bit thin, suffice to say.
DH was worried about this same issue. Would our landlord try to stop us if we told them? Would the neighbors call the apt manager, or worse, the cops?
My take on it is, there is some concern maybe for the apt manager trying to stop you before hand. But honestly, everyone here is dead on. They've no leg to stand on with that nonsense. My take on it is, we made this baby in our apartment, didn't we? We can birth it here too.
As for the neighbors, if you choose not to tell them beforehand, a sign is a good idea. I kind of fall back on the idea that you'd have to be a pretty gigantic jerk to see a sign like that, then still elect to call someone to try to interrupt someone birthing. I mean, that's pretty cold, my friend. I don't think most people are that, well, ballsy. At least they aren't in the midwest where we're from.
And I tend to take full advantage of that.