That is an excellent question. I would venture to say yes legal to own legal to carry. However heres the disclaimer....
I am not a lawyer don't do it till you ask one. Later in the day I am sure someone will come along and cite laws, facts and figures. I have looked but all I can find is they don't need to be registered, can be bought without a pistol purchase permit and generally don't have S/N.
I would say carry a registered firearm. Just for the reasons above. Not to mention reliabillity, reloading time, and other factors. But if its all you have I would suggest contacting the state police first they may be able to at least set you in the right direction. Go to the MSP website look for the "contact MSP" and shoot them a email. Can't hurt, might help.
Oh and not everyone can open carry. You must be at least 18, and the handgun you are carrying must be registered to you. You can't be a felon i.e. you must be able to own firearms. Check out Michigan Open Carry website theres a lot of great information there that will help you understand the laws of open carry. And i suggest you know the law backwards and forwards before you open carry, anytime you are armed you are either 100% within the law or you are 100% wrong. Knowledge is power!
Also if your able try and make one of our seminars, they are very informative and as a plus you'll get to meet fellow OC'ers. Win win!
And WELCOME to OCDO!