The police officer you encountered is actually a Loss Prevention employee for Best Buy, unless they had a uniformed police officer in the store that day. Most likely Best Buy has a $ threshold that is slightly higher than the amount you allegedly stole, which is why they didn't have you arrested and charged. Thus, they opted to have you banned from their store(s). If this is the case, consider yourself lucky, as you were not prosecuted for a criminal offense. I would advise you to stay clear of all Best Buy stores, or else you may find yourself being arrested and charged with criminal trespass (and possibly a criminal record).
However, are you positive that the document you signed only stated that you were banned from Best Buy, or did it also contain information about a Civil Demand?

