I was told by someone who was looking up stuff for the earliest Catholic records in Bay County and she told me that the diocesan office holds the records now and they wouldn't--even after intervention by several priests and the priest-administrator--even consider letting her look at the files. St. Joe's records are in the church and you can see them 1 hour each week and they do the lookups. St. Stan's might be better seeing as they are one of the largest in Bay City. Good luck!! The cemetery office has been very helpful for me in their records and the cemetery readings and tombstone pictures are online at www.mifamilyhistory.org/bay/
Hope this helps.