In my experience, in Minnesota, police and the courts will want fingerprints from people charged or convicted of "a targeted misdemeanor" such as domestic assault. When I have had cases where my client was charged with domestic assault on a Summons (had not been arrested and booked, including fingerprints), and for whatever reason the case was resolved as a Disorderly Conduct or better, I have usually been successful in asking the judge to Order that my client not be fingerprinted, since he had not been convicted of a targeted misdemeanor. It is my understanding that they will get an arrest warrant to fingerprint you, in this situation, unless you take the affirmative step of going to court and getting a judge to Order that you are not required to, presumably for the reason just stated above. You would do better in this request if a lawyer made it for you. Contact the lawyer who represented you, or the Public Defender if they represented you then.
Fingerprints are required for Targeted Misdemeanors. I agree with my colleague's recommendations. You should either get fingerprinted or seek a court order excusing you from having to supply prints. Depending on how your case was ultimately resolved, you might be eligible to have the arrest records and fingerprints sealed.