You have no right to free service of process by law enforcement. Rather, you need to retain someone (lawyer, and/or a process server company in Minnesota--i.e., a company that specializes in personally serving papers) to serve the papers and provide an affidavit of service that you can submit to the Court. The cost will vary depending upon the difficulty and time it takes to serve the papers.
More importantly, why are you trying to do this on your own? If you are in some kind of family court proceeding, you need a lawyer to help you navigate through these matters.