(1) Civil process in the district court shall be served by a sheriff, deputy sheriff or a court officer appointed by the judges of the court for that purpose, except that officers of the department of state police or conservation officers of the department of natural resources may serve civil process in any action to which the state is a party and police officers of an incorporated city or village may serve civil process in any action to which the incorporated city or village is a party.

    (2) Under rules of the supreme court, any other person may serve any process or order of the district court that does not require the seizure, attachment, or garnishment of property or the arrest of a person. This section applies notwithstanding section 1908.