Yeah. MN statue 169.011 sub 45:
"Motorized bicycle" means a bicycle that is propelled by an electric or a liquid fuel motor of a piston displacement capacity of 50 cubic centimeters or less, and a maximum of two brake horsepower, which is capable of a maximum speed of not more than 30 miles per hour on a flat surface with not more than one percent grade in any direction when the motor is engaged. "Motorized bicycle" includes an electric-assisted bicycle as defined in subdivision 27.
For the majority of things that cross my desk it's the horsepower rating that makes them motorcycles. There are a surprising number of peds out there that are limited to 30mph but make 2.5 or even 4 hp.
The reason that so many dmv offices give out moped plates to vehicles that dont qualify is that many MCO's (manufacturer certificate of origin) will list the cc's but no other info, in which case they rely upon the customer certifying its speed and hp. If it ends up being registered incorrectly it's an issue for the cops, rather than DVS. We just maintain records, we don't enforce.