Marijuana is illegal in the state of Michigan. Possession outside of the medical marijuana program is a criminal offense and could lead to jail time. There are no special laws for visitors to the state. There is a medical marijuana program that offers reciprocity to states that offer reciprocity to Michigan medical marijuana cardholders.
If you have a medical card from your state and are visiting you will be treated the as a Michigan card holder, and must follow and adhere to the same laws accordingly. If you do not have a medical card marijuana is still illegal and a misdemeanor or more in the state of Michigan. The only exception is Ann Arbor where it is decriminalized and only a small fine.
Michigan only allows legal marijuana use by those who hold a Medical Marijuana Card. Possession of marijuana in Michigan can lead to fines or incarceration, depending on the amount of marijuana in your possession. These are state laws and compliance with them is no different for tourists than it is for Michigan residents.