If you were no charge was ever filed or one was filed, but probable cause was never found, then the best kind of expungment should be avaialbe under Minnesota Statutes 299C. Or, otherwise, if you were a juvenile certified as an adult, certain first time drug charges, or did not plead guilty and were not convicted, then should be eligible for expungment under Minn Stat Ch 609A. See links below:
As my colleague noted, if you were convicted it is very difficult to get a criminal record expunged in Minnesota. If you were charged and acquitted, or the case was dismissed, then you would have an opportunity to seek expungement, but if you lost at trial or entered a guilty plea, the statute makes it quite difficult for the court to expunge or seal the records.