You were never convicted of a DUI in court because the charges were dismissed in Court. You should then have your charges expunged (removed from your record) if you have never been previously convicted of a crime. Then you can lawflly and legally say that you have ever been arrested to private employer's. As to potential government employer's, they may be able to see that you had something expunged, but not the details of the case. You should be aware that with a DUI there is an administrative hearing with the Department of Motor Vehicles and, if your license was suspended at that hearing, it will show up as a DUI on your driving record and the employer will find out if they pull your driving history record.
If the charge was dismissed then you were obviously never convicted of the DUI. If this was the only case you've ever faced then you can honestly tell an employer you have never been convicted of a crime.
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