Here's the official Michigan State Police pdf on open & concealed carry. Anyone is allowed to open carry.
http://www.michigan.gov/documents/msp/MSP_Legal_Update_No._86_2_336854_7.pdf
And here is a link to the law that applies to
non residents... the actual law itself that dcselby1 mentioned...
Michigan Legislature - Section 28.422
FIREARMS (EXCERPT)
Act 372 of 1927
28.422 License to purchase,
carry, possess, or transport pistol; issuance; qualifications; applications; sale of pistol; exemptions; nonresidents; basic pistol safety brochure; forging application; implementation during business hours.
Sec. 2.
(1) Except as otherwise provided in this section, a person shall not purchase, carry, possess, or transport a pistol in this state without first having obtained a license for the pistol as prescribed in this section.
-snip-
( 8 )
An individual who is not a resident of this state is not required to obtain a license under this section if all of the following conditions apply:
(a) The individual is licensed in his or her state of residence to purchase, carry, or transport a pistol.
(b) The individual is in possession of the license described in subdivision (a).
(c) The individual is the owner of the pistol he or she possesses, carries, or transports.
(d) The individual possesses the pistol for a lawful purpose as that term is defined in section 231a of the Michigan penal code, 1931 PA 328, MCL 750.231a.
(e) The individual is in this state for a period of 180 days or less and does not intend to establish residency in this state.
-snip-
so basically a non resident must meet the criteria stipulated above in order to legally .. carry.. transport... or even possess.. a pistol in Michigan.