If it simply says “In a Relationship,” but no person is listed, she is likely actually in a relationship, unless she does not use facebook frequently and simply hasn’t updated that she is single again after a breakup.
IF, however, she is listed as in a relationship with a specific person, there is a reasonable chance that the relationship is not legitimate. For instance, my facebook profile actually says that I am “Engaged” to my friend Julie, and we’ve been facebook engaged for about four years now. In reality, I am a straight woman in a serious relationship with a man. My facebook engagement with Julie is simply a reflection of a fun, girly friendship.
A large portion of my facebook friends are in these type of jokey facebook relationships with their good friends. Many straight women are “in a relationship with,” “engaged to,” or “married to” one of their good female friends. I also have a number of female friends who are in a facebook relationship with one of their gay male friends. And, perhaps strangest yet, there are even straight female women who are in jokey facebook-only relationships with straight men! These pairs may be simply good friends who wanted to make a silly facebook relationship with each other that isn’t actually reflected in their true romantic lives.
As for how to proceed, my number one piece of advice would be to not say something corny and stupid about her facebook status like, “So… are you still in a relationship?” or “Who’s the lucky guy?” Ugh. Horrible.
Just take it easy, continue talking to her, and let things unfold naturally. Don’t mention the facebook relationship status either way. Don’t flirt with her too overtly until you get a sign from her that flirting would be okay. Continue being friendly, and you should naturally find out whether she is actually in a relationship through your conversations.