Donnie,
Your ancestor has a CMSR under the name J.M Routon. His name is also listed within as John M Rowdon and John M. Rowden. It indicates service in Co. K., 37th Alabama Regiment. It does not give his date of enlistment, so that cannot be crosschecked against the information given in the widow's application. His capture and parole at Vicksburg is confirmed in the documentation. The only other information in the file is in reference to his discharge which was given on Surgeon's certificate of disability, but the original paper, which would likely provide details, is not in the file. He appears on a register of payments to discharged soldiers giving the date of discharge as Oct. 15, 1862, and the date of payment as Oct. 16, 1863. It does not state the place of discharge, so again we cannot crosscheck the place as Spring Hill, but can say that it was not in August as the widow stated. These forms, filled out so many years after the war by widows (or even by soldiers) often misstate the dates and places. There were many deaths from disease in the unit in 1863, and also deaths and injuries from battles. Without a document in the file we cannot know the actual reason for his disability. The date given above is not long after the unit was in the Second Battle of Corinth and the Battle of Hatchie's Bridge, so it could have been due to wounds received then or earlier. I did confirm the service of the two men who signed the application as witnesses. Both were in Co. K. M.V. Gibson served as a private, while M. W. Carroll was a sergeant.

You may order copies of the CMSR here: http://history-sites.com/research/

A comprehensive summary of the history of the unit can be found here on a site maintained by Chip Culpepper, a frequent contributor on this board.
http://www.alabama37th.com/History-a.htm