Danny,
I agree that regimental histories available on-line do not mention Perryville, however, in addition to the CW Research Data Base, Alton, Ill POW records show at least one 37th Miss. POW captured at Perryville.
George Martin
Alton Prison [http://www.altonweb.com/history/civilwar/confed/j.html]
Name
Rank, Company, State
Date and Place
of Capture
Date of Death
Cause of Death
Place of Burial
Jackson, W W
PVT, H
37th Mississippi
10/11/62
Perryville, Kentucky
........................
From the CW Research Database
Warren W. Jackson
Residence was not listed;
Enlisted as a Private (date unknown).
He was listed as:
* POW 10/11/1862 Perryville, KY
He also had service in:
"H" Co. MS 37th Infantry (Died of variola)
Other Information:
Buried: Confederate Cemetery, North Alton, IL
...................
Personnel from the 37th MS Infantry
who were wounded at Perryville, KY
4 Rows Found i.e., four deaths are listed [as I previously noted] with name, Co., etc.