I agree with the other two. Definitely sing something from a musical, but sometimes they will ask for a rock song also (maybe auditions for Tommy or Hair.) Unless assigned to, do NOT sing a song from the show that you're auditioning for. If you do that, you are a) looking like you have limited knowledge of theatr b)forcing yourself in that role when you might be better in another - it shows lack of versatility. Let's say you Carrie in Carousel, but you might make a better Julie. That way the auditioner can ONLY see you as the forced Carrie.
Rosencrantz: "Be happy - if you're not even HAPPY what's so good about surviving? We'll be all right. I suppose we just go on."
- from Tom Stoppard's Rosencrantz and Guildenstern are Dead