Elevator talk?

Ask, "Did you fart?"
lol just kidding. I would've laughed and said yes though.
Anyways,
Ask if she works there (if business bldg), or ask if she goes there often (mall), or ask if she enjoyed her shopping (mall, with shoppin bags), or ask how her day is going, just ask something casual.
Or, something sweet you can ask is "Dont want to sound rude, but your perfume smells really good." If she's cool, she'll smile and say thank you, then you can start a conv from there. If you run out of time to talk, you can always get off at whatever floor she's getting off of and continue talking to her.
P.S. I recommend talking to her if it's just you and her in the elevator. She might feel uncomfortable if a lot of people are around.

how's life? seriously I met a guy on the elevater when I was asked that exact question. never forgot him.

"So where you headed? First floor? Second? Oh! I'm stopping off there. Want a ride?" >_>

I really think there is no right answer. I work in a 22 story building and this happens to me a couple times a week. When the girl says something first you play off that. I find just saying hi and reading there reaction is the best approach. You will know in 2 seconds if she is into it or not. the problem is if she is into it you have 30 seconds or less to seal the deal because the ride is so short. It is really one of the harder situations to be in because good or bad it starts and ends quick. Just once the ice is broken move quick.