You can email your request for a look-up in the Detroit City Death Index at the Burton at the following. http://www.detroit.lib.mi.us/featuredcollection/burton-histo...
They usually get back to you in a few days but they will be closed for the holidays so I would give them a little more time.
The Burton also have indexes to Wayne County Deaths, excluding the City of Detroit, online from 1934-1953. They are located under "Resources".
The Mormon church has finished indexing the Michigan County Death Records 1921-1951 or 1952. They are still going through arbitration but I am hoping they will be available next year sometime. Their website is www.familysearch.org