If you were at the store, you must have a pretty good idea of (a) why they think you were shoplifting, and (b) how they figured out who you are and how to contact you. You will also know (c) if you were shoplifting.
Based upon that information, you can assess whether this is a legitimate demand, and whether you want to risk being charged.
A store should not be telling you, "Pay a civil demand or we'll charge you". Perhaps you could clarify exactly what happened.

