I'm assuming from your question that there is no prosecutor (or solicitor) involved due to the type of court you are in. If there is a prosecutor (or solicitor), then they can continue the charges against you despite whether the owner or the cop want to prosecute. Now if there is no prosecutor (or solicitor) and it is just the cop who is the opposing party, then the same would be true. The cop can continue to bring the charges even though the owner does not want to prosecute. In a situation like this you may have a number of options, which you should consult an attorney about.
If the authorities have been notified of your shoplifting offense, the ultimate decision on whether to prosecute you or not will be made by the State Court Solicitor (unless you have prior shoplifting convictions and the charge has been elevated to a felony.)
In any criminal case: violating a criminal statute is viewed by the State prosecuting authority as committing an offense against the good peace and order of the State of Georgia. The store owner will generally have a great deal of input as to whether you are ultimately prosecuted. But it is not unheard of for the prosecuting authority in your jurisdiction to ignore a victim's wishes and proceed with a criminal prosecution.
If you were arrested then in Florida the decision whether to go forward with prosecution rests with the State Attorney, only. As a general practice in our area, however, the SA would most likely honor the expressed wishes of the victim and would drop the case. Florida law requires that the State Attorney give "great weight" to the victim's position as to prosecution and the disposition of any case.
