You should speak with a criminal defense attorney in your area in Georgia. Besides getting the charge dropped, you may want to see if it is possible to have your record expunged as a minor, or maybe the record sealed. I practice law in NY, so you should check with a Georgia Attorney. Good luck.
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If you have a public defender, that attorney should be able to tell you how or if you can get your underage drinking charges dropped.
Without seeing all of the evidence, I couldn't tell you what your chances are of the case being dropped. Don't be suprised if the officer says he/she could smell alocohol on your breath, which could be enough evidence to convince a prosecutor to pursue the case. Contrary to many things you'll see on tv, Public Defenders are very good attorneys and unless you have some reason to be unhappy with yours, that public defender should be able to get you a result as good as any other attorney.
"Dropped" is a pretty wide open concept: you're actually asking a very broad question. So let's begin at the beginning to figure out how to get your underage drinking charges dropped.
1. "I was never breathalyzed or ever admitted to drinking." If I had to guess, the officer probably wrote on your ticket "Minor in Possession (By Consumption)", or some variation thereof. Although it sounds like you weren't observed drinking, and you didn't take a breath test or admit consuming alcohol, the officer probably smelled it on you and made his case based on that. Without seeing your ticket or knowing any more facts, it's possible his theory is "If I smell it, that means you drank it. If you're under 21, you're busted."
2. By "drop", you probably mean dismissed. Sure, any charge can be dismissed: the question is, can your lawyer or you convince the officer or the prosecutor to do that? You were in Athens, and hundreds of these types of cases are made in Athens every year, meaning the courts are familiar with them and used to seeing a certain amount of evidence from these cases. That also means the officers have learned what judges will accept in a case. If the officer didn't attempt to gain more evidence from you by asking you to take the state test, I imagine that means it's because he either didn't know he needed more evidence or he felt he didn't need any additional evidence to make his case stick. The law is hard and fast on who can drink and who can't, but there are some exceptions: you can read them by going to Official Court of Georgia Annotated section 3-3-23. A lawyer who is familiar with the law will be able to advise you about the elements in the charge (what the state has to prove to find you guilty) and the affirmative defenses in the law (the things that make drinking under 21 permissible). A good lawyer will take the law as it's written and apply the facts in both the best and worst possible lights to give you a total idea what types of problems you're facing and what types of problems the State will be facing in trying to prove this charge.
3. To "drop" a case can mean different outcomes: the case can be dismissed; or you can be given pre-trial diversion, which could end in a dismissal in exchange for community service and a few other tasks on your part; or you can utilize a type of plea that can result in a dismissal after you have entered your plea and completed a term on what is called 'first offender' probation. Whether any of these things happens depends on the facts as you relate them, the facts as the officer remembers them, your prior criminal history, and the normal procedures of the court and judge in handling these cases. So "drop" can mean many different things.
Of course, the best thing to do is to meet with a lawyer. Lawyers familiar with the subject will be in a great position to give you true advice on how to proceed. Many lawyers offer free consultations, so take advantage of one. Good luck!