The county of Monroe is unique, because they had many gaps in recording the Naturalization records in the county. Records are stored in two separate locations. They are the Common Pleas Court and the archives in Lansing.
The records at the county level are located at the Common Please court in Monroe. Dates are sporadic on their coverage. Here are the dates from the archives and they will be the same at the courthouse. 1849-1929. Be sure to check ahead prior to looking for your records to make sure your relative falls within these dates. Another place to check would be the neighboring counties and Toledo. They have no letters of intent.
Searching for these types of records in Monroe Co will be a challenge. Have a great day.