Unfortunately for genealogists in the State of Michigan there are some pretty strict laws protecting birth records. You are in luck that your birth record is over 100 years old...before that they are protected by law except under certain circumstances.
There is a request form for the Grand Traverse County Clerk on the website:
http://www.co.grand-traverse.mi.us/departments/county_clerk/...
You can send it to the clerk's office directly with payment. If they don't have it on file they send you back your payment...or they used to. It's worth the $10 and the stamp. Good luck. Let me know if I can be more help.
Alanna