When searching for information about your town, check county and Michigan sites as well as the city/township website. Towns, hospitals and schools often report data to the county or state and don't necessarily publish the same data on their own sites.
What to look for on county/city/township websites
District courts are organized by county. Larger counties will have several for the county. Example: Oakland County
Court websites vary in the information they provide. Some offer livestreams, court documents, etc.