Call the Dearborn City Clerk's office. They have an index to Dearborn deaths. At least they did when I called several years ago. They might have changed their procedures to raise more money.

http://www.cityofdearborn.org/government/city-clerk

City of Dearborn has death certificates for those who died in Dearborn and they are cheaper than the State of Michigan which now charges $34.00.

That's odd that the Michigan Death Index only shows the year. I thought they showed the actual date of death as well as the place of death.