This means that you successfully completed a diversion program and the State Attorney dismissed or nolle prossed the case against you. You can get the certified dismissal from the clerk of court in the county where the case originated. Completion of the program takes care of the charges but it does not mean you are not guilty. That is a legal term meaning a jury or judge listened to the facts and applied the law and came to the conclusion that the state had failed to prove the charge against you. That did not happen here. It would appear that you qualify to get the charge expunged and I would recommend you do so. Contact a lawyer to handle it for you and be sure it is done properly.
The Nolle Prosequi is the document that reflects your charges being dropped. If a copy is not sent to you, you can go to the Clerk's office and get a certified copy of it.
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The Notice of Successful Completion and Nolle Prosse is the proof you need to show the case was dismissed. Deferred Prosecution Agreements (or "DPAs") are usually extended to people with little or no criminal history, so you may be able to have your record expunged, however there are numerous obstacles to expungement. The Florida Department of Law Enforcement (FDLE) has a question and answer page on their website regarding expungement and you may want to start there if you are considering taking that course of action, however it is always in your best interest to seek the advice of a lawyer when deciding how to proceed.
You can go to the clerk of court and request a certified copy of your disposition. This will be your written verification that the case has been dismissed. In addition you may use this document in the process to expunge your record as along as you are otherwise eligible.