I wouldn't ask if she is in a relationship - because if she is, it would be awkard for you both. But then again, as others have pointed out - why would she go for a coffee with you?
See how things go - if she likes you, she'll hold eye contact, play with her her a little (not like nervously) mirror your body language and she'll smile/laugh a lot when talking to you and her attention would be only on you - eg not glancing around the room as you talk to her and she wouldn't admire her finger nails
Good Luck with everything
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