Wthout more facts it would be very hard to say.  However most retailers are privelaged against this type of lawsuit if they believe someone is stealing

Although I do not practice law in the State of Michigan, here are my initial impressions.  First, are you asking whether this would be sufficient for a law suit against the store, or sufficient for a lawsuit against your daughter?  Obviously, first it is necessary to determine whether your daughter was actually arrested as a result of the accusation.  If she was, then you would only have a suit for false arrest once her criminal charges were found either not guilty or dismissed.  If she was not, then chances are there are not sufficient damages to justify a suit against the store.  In any event, if your daughter feels that her rights were violated, or if she has pending criminal charges, she should hire an attorney.  Good luck.