A little confusing. If you did not plead guilty, or were found guilty, a dismissal means the charges are dismissed. That is a very good thing. In NJ, I still move to expunge a record of a dismissal, so that it does not appear on the client's record. An attorney in your state can let you know the laws there on this issue.
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You can tell employers that you have not been convicted of a crime, but the case may show up on the court's records, with the notation that charges were dismissed after successful completion of DEJ.
There is no way to get the matter removed from your criminal record. It will always appear on your criminal history, or "rap sheet." The only way to get an entry removed from your rap sheet is to get a finding that you were factually innocent, and you are not eligible because you entered a guilty plea.
You added a comment that you are a Legal Permanent Resident (LPR, or green card holder), which raises some concerns. Theft is a crime of moral turpitude, which can lead to removal (deportation), denial of citizenship and permanent exclusion from the United States.
Until a couple of years ago, the Ninth Circuit Court of Appeals recognized DEJ dismissals in cases where you entered a plea, but the case was dismissed. Since your case was dismissed prior to July 14, 2011, you should be safe, but you could encounter problems if you leave the country and try to reenter through a port of entry that is not in the Ninth Circuit, which includes Alaska, Arizona, California, Hawaii, Idaho, Montana, Nevada, Oregon and Washington.
You may be able to avoid immigration consequences through the petty offense exception, which will excuse one minor offense. You might also be able to set aside the plea (even though it was dismissed) if you were not advised of immigration consequences.
I would recommend a consultation with a criminal defense attorney who has also taken the time to study immigration law. While the US Supreme Court says criminal defense attorneys have an obligation to advise clients about the immigration consequences of a plea, many lawyers do not make the effort to obtain the necessary education.
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