I was going by what their website said. I would try calling but not on a Monday or Friday. The trouble with calling is that you have to hear about the City Clerk every time you get transferred to another option.
I worked on indexing the Michigan County Death records from 1921-1951 or 1952. They have all been indexed as of December and most of them have gone through arbitration. If you can wait awhile, they will be available on the Mormon Church's website-www.familysearch.org
You will be able to download the image for free rather than having to pay a fee-the State is either $26.00 or $27.00 if you know the date of death. Otherwise, they charge $12.00 per year look up on the top of the original fee.