Ohio issues marriage licenses at County Probate offices. One thing to keep in mind while filing for your marriage license in Ohio, is that one of the parties has to be from the county you are obtaining your marriage license from. For example, if you wanted to get your marriage license from Adams County, you or your fiance must be a resident of Adams County. If both parties are from out of state but wish to be married in a particular Ohio county, the couple must get their marriage license in the county they wish to be married in.