I would compose myself and calmly find out what the interview is about. If I am comfortable, then I would go ahead with it, thinking before answering to be sure of myself. If I am not comfortable, I would walk off in another direction.
I've done it... but really didn't want to! I was interviewed regarding an accident that I'd witnessed. Saw someone drive a car into a house; it went right through, you could see into the living room... it was crazy! Don't really remember what I said about it, though -- that was over 20 yrs. ago!!
If you don't have any warrants outstanding and you haven't jumped bail or anything, go ahead and talk to them but be careful, they have ways of wording questions and editing answers to get you to say what they want.