No, according to Federal law, you are not allowed to both use medical or recreational marijuana and have a Michigan Concealed Pistol License (CPL). This is due to a conflict in state and federal law.
Michigan is not the only state facing this dilemma. For example, a man in Pennsylvania has filed a lawsuit seeking clarity regarding gun ownership rights. According to the HuffPost,
A medical marijuana prescriber and patient is challenging President Donald Trump’s administration over a federal statute barring cannabis users from purchasing or owning firearms, even when they take the drug legally pursuant to state law.
A similar lawsuit was filed in Nevada, and in that case the court ruled in favor of the government. It seems likely that this issue won’t be resolved until marijuana is made legal at the federal level, or at least removed from schedule one. The last time this came up the attorney general decided to keep marijuana on schedule one, so it may be some time before gun owners see this change.
The problem arises because the 1986-gun control act states that any unlawful controlled substance user is also prohibited from owning or carrying a gun. Specifically, federal law currently prohibits the possession of a firearm by anyone that uses or is addicted to a controlled substance. Any time you attempt to purchase a gun, you will be required to complete form 4473, which also requires you to disclose your use of marijuana. It’s a Catch-22 because answering “yes” to the drug question on the 4473 will disqualify you from purchasing the firearm. This is because marijuana remains a scheduled one unlawful drug on both the state and federal drug statutes and as such it remains an unlawful controlled substance. This is true even though the recreational and medical and possession of marijuana is now completely legal in Michigan.
Medical marijuana users are at a heightened risk because their use is “on record.” Simply applying for the medical marijuana license means that state government and perhaps the federal government both “know” you are a marijuana user. However, recreational users are also at risk because if they come into contact with law enforcement who, as part of an investigation learn of the marijuana use or possession, they could report same to the National Instant Criminal Background Check System (NICS). Thus, the gun seller who checks the NCIS as part of a background check could already know about your marijuana use even before you fill out the form.
Consequently, Michigan medical and recreational marijuana users will need to make a choice, use marijuana and lose the CPL or keep the CPL and lose the marijuana.