To the best of our knowledge in Minnesota seat belt violations do not show up on your MN motor vehicle record (MVR).
Minnesota statute 169.686 (SEAT BELT USE REQUIRED; PENALTY) states that a properly adjusted and fastened seat belt, including both the shoulder and lap belt when the vehicle is so equipped is required of the driver of a passenger vehicle, or commercial motor vehicle; a passenger riding in the front seat of a passenger vehicle or commercial motor vehicle; and a passenger riding in any seat of a passenger vehicle who is older than three but younger than 11 years of age.
The statute continues on saying that a person who is 15 years of age or older and who violates this statute is subject to a fine of $25. The driver of the passenger vehicle or commercial motor vehicle in which the violation occurred is subject to a $25 fine for a violation. Of course if you were ticketed as a passenger for a no seat belt violation than contact the court for the amount of your fine since usually the base amounts listed in state laws have court fees and other costs added onto them making them more expensive than just the $25 listed in the state statute.
The MN seat belt law is a secondary one, though there is a push in the MN legislature to make it primary, meaning a peace officer may not issue a citation for a violation of this section unless the officer lawfully stopped or detained the driver of the motor vehicle for a moving violation other than a violation involving motor vehicle equipment. If it becomes a primary offense than police could stop you for not wearing your seat belt and not need to stop you for another offense such as speeding as they do now with it being a secondary offense.
The MN Department of Public Safety does not record a violation of this seat belt law on a person's driving record. The DPS explains that fines collected from violations of this law go into a dedicated account that goes mostly to the emergency medical service districts. These EMS districts are to use the monies received for personnel education and training, equipment and vehicle purchases, and operational expenses of emergency life support transportation service.
Since this violation in Minnesota does not go on your driving record the insurance company would not see it on your MVR so usually would not rate on it.
Update: On June 9, 2009 Minnesota's seat belt law became a primary offense. This means drivers and passengers in all seating positions, including the back seat, must be buckled up or in the correct child restraint. Law enforcement can now stop motorists solely for seat belt violations, including unbelted passengers. Before this was a secondary law and police needed another traffic reason to stop you, such as speeding, in order to find that your seat belt was not on properly and ticket you for that offense. Now in MN law enforcement can pull you over and cite you just because they see your seat belt is not on properly.