This is the URL to fill out and print your application. The form is in PDF format and once it opens you can type into the form on screen. Send it to the address listed, in East Lansing, and it should be processed this time of year in less than 3 weeks. If you have any questions, use the phone number on the form and speak with Jill in the Communications Office - weekdays only, 9 AM to 4 PM, eastern time.
http://www.michigan.gov/documents/com-022_8561_7.pdf
I'm not a resident of Michigan but received mine for those times that I have to respond into the U.P. as a Public Safety Chaplain. It is issued for life unless you violate the provisions of the permit.