Unless you're really good at reading people, you probably can't by looking if she's just shy or if she's depressed or if it's something else. She also might have a boyfriend.

As far as talking to her, I don't think you could go wrong by making small talk about the class you share and see what happens. That way, even if she doesn't want to talk to you, it's not your fault. At least, that's how it would work where I live (in the southern US.)