does anyone know the laws in michigan about transfering moped registration from one motorized bike to another because my bike frame broke and I need to tansfer my kit to another bike frame
Well if it's like any standard law the general rule is No you can't, until you've spent too much money, at least.
I'd probably say it was safe to install the engine into another bike, since they made it easy enough for you to even get one of these legalized. Probably a good idea to keep the same color and make, and lastly I would remove the section of frame with the serial number if they keep track of that and fix it to the new bike somehow.
Seriously if your able to get plates and insurance on one of these then the only reason why you'd be stopped by an officer is if you make a driving boo-boo, and even then I seriously doubt he will be questioning the authenticity of your bike all the way down to checking vin numbers or something silly against the vehicle records. It's when it's different color and brand than recorded does it start looking suspicious to anyone.
Again it's not really possible to change the registration to apply to what is technically another vehicle, the titling process is simply creates a record of a legitimate vehicle that acts as a buffer to ensure insurance coverage is being met and that inspection is also being done, it's meant to trace a single plate back to a single vehicle and therefor to a real person. When a vehicle is considered wrecked then the state registration is there to make sure you don't just sell a ruined beater to a naive person, so it's marked as being busted until an inspector can pass it as a rebuild.
I guess the problem is that if you transfer a registration then what you are doing is publicly announcing that a bike existed for a time, then disappeared entirely from existence but the identity of that bike should be adopted by this other bike that now also came out of no where, and that everyone should act as though nothing has changed while the new bike isn't actually as I say it is. Almost the equivalent of removing the skin with your finger prints and grafting it on another person and then handing them the matching birth certificate and ID card.
If it were me I'd probably buy a much better bike and just bite the bullet and Register another bike, when you live somewhere where it's just not as simple to get a bike made legal you can really appreciate such lax laws. If you registered again then you don't have to sweat reporting it stolen to the police since if they do find it they wont pop open a can of worms while running numbers..