Under current Minnesota law, you cannot expunge both criminal and civil records if you entereed a plea of guilty to the charge. As a result, even if you wait a year, you will not be able to remove the charge from all records.
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Two years is a long time. Of course, it's best to anticipate the nightmare of having a criminal conviction on your public records, even a minor one; and retain a good lawyer in the first place to work to avoid it. It is possible to ask a court to allow withdrawal of a guilty plea, or reopen a petty misdemeanor case. The passage of time, however, would make this more and more difficult. You could try anyway. Best to have a good lawyer's help with it.