Is it a bad idea to approach someone who lives in your building?

I know that people say you shouldn't approach a girl at gym or at your work.

But should you approach her if you see her often in the elevator? Or if she is your next door neighbor?

Wouldn't it make things awkward next time if she rejects you?

I have a cute neighbor and I see her in the elevator from time to time. She lives right next door to me. She smiles and says hi but never talks to me.