How are multi vs single engine helicopters categorized?
For the FAA, rotorcraft powered by more than one powerplant are not separately classified.

A random N-number search for a random twin-engine helicopter—AgustaWestland AW109—using the FAA registry yielded the type as: Rotorcraft.

However for a Boeing 707, the type came back as: Fixed Wing Multi-Engine.

I couldn't find a place where the different classes are listed on the FAA website, whether for fixed-wing or rotorcraft.