Luckily, the Livingston County Sheriff Dept is fairly nice on that. When I got mine, I went through a background check, and then got my permit to purchase(10 days valid). I then bought the gun with it, and went back to the sheriff's dept to get it registered, I mean "safety inspection". The clerk passes the gun around to the undersheriff and others at the station who then marvel at how cool the gun is, and then give it back to me, no charge.
There is no 'one gun a month' law here, but I think you need a permit for each pistol since the gun is what is registered.
It was easy HERE, but I heard it was harder in some places, notably Wayne County.
From the NRA-ILA Michigan law site:
"To purchase a handgun from either a dealer or private individual, the buyer must obtain a license to purchase from the chief of police if the buyer lives in a city, or the county sheriff if he lives in an area without an organized police department. The buyer must be 18 years of age, a U.S. citizen, a resident of Michigan, have no felony conviction, have never been adjudged insane (unless later restored by court order), and score 70% on a basic pistol safety review questionnaire.1
The license to purchase must be filled out in triplicate at the time of purchase. The license shall include a description of the handgun sold and the signatures of both the buyer and seller. The seller may retain one copy and the buyer retains the other two. After purchase and delivery of the handgun is completed, the buyer must return the license to purchase along with the purchased handgun, unloaded and encased or trigger locked, to the local licensing (law enforcement) authority within 10 days.
The buyer (licensee) will then be issued a safety inspection certificate (registration) for the handgun. One copy of the license will be held by the local authority for six years and the remaining copy shall be forwarded to the Commissioner of State Police. The license, once issued, becomes void if not used within 10 days."
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Sounds pretty infringing to me. FWIW, I've purchased three handguns in Texas. The first two before the Brady Instant Registration went into effect. In all three cases I walked in with no paperwork, and walked out in no more than 15-20 minutes, required to fill out the federal forms, and in the later case, wait for the Instant check, which pretty much was.