As of August 1, 2018, it against the law in Minnesota to use fake service animals. The new offense makes it unlawful to to intentionally misrepresent an animal as a service animal in an attempt to receive the same rights and privileges as someone who qualifies as disabled under the law and needs a service animal.
Although the first violation is a petty misdemeanor, repeat offenders can be charged with a misdemeanor crime.
You can read the new law here.