I found a baptism for Martin Schmitt in the transcribed church records of Ss. Peter and Paul Catholic Church in Nenno, Washington County, WI. The chance of finding a birth certificate that old are slim.

Martin Schmitt
born June 25, 1859
baptized July 16, 1859
Parents: George and Margaretha (Wetterich) Schmitt
Sponsors: Martin Fechter and Maria Schmitt

I checked the rest of my transcribed church records for additional children, marriages, deaths, or cemetery listings. I did not find any for George or Margaretha. There appear to have been several other George Schmitt or Schmidt's in that area about the same time. These had other wives than Margaretha. Maria Schmitt might be a sister of your George Schmitt.

Good luck!