It depends on how the case was resolved. If it was resolved without a guilty plea and without a conviction (such as a "Continuance for Dismissal without a plea"), and the charge was ultimately dismissed, then you should be able to get an effective, statutory expungement under Minnesota Statutes Chapter 609A. See links below for more.
I agree and will add that if you did enter a guilty plea, the challenges of getting a worthwhile expungement certainly increase. However, it may not be a hopeless cause depending on your circumstances. It is best to consult with an attorney individually for tailored advice. You could try to pursue an expungement alone, but I do not recommend it since the process can be tricky.
I agree with my colleagues. The main issue is how your case was resolved. If you never entered a guilty plea, then you have the right to seal the records. However, even if you entered a plea of guilty, you still might have an opportunity to seal all of the records. There is a case currently under review which may have an impact on the expungement/sealing process. I would encourage you to seek good legal advice regarding your options.