Chris, first off welcome to the site, now to your question, guest is right as far as registering a boat and having hull numbers, but I think you're talking operating a boat, in that case everyone is required to have the operator card regardless of motor size.
Seems silly to have to have the card to put a trolling motor on my canoe. I can paddle as fast or faster than the motor will make it go! If the rule should be any boat if this is a saftey concern. Can you say Tax Grab.