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Minnesota has written a tiny house code fact sheet:

If the tiny house does not:
• have a chassis and axles, or
• have a HUD manufactured home label, or
• have a RVIA park model label, then
• it is either a prefabricated or industrialized modular building subject to Minnesota Rules Chapters 1360 or 1361 or
site-built subject to Minnesota Rules Chapter 1309.

NOTE: Any modular unit of closed construction built away from the site of occupancy must be labeled (Minnesota Rules,chapters 1360 or 1361).
Closed construction means any building manufactured so that all portions cannot be readily inspected at the installation site without disassembly, damage to, or destruction thereof (Minnesota Rules, Chapter 1360.0200 Subp. 5).

Full text:

Also here: Minnesota Tiny House Fact Sheet