Shiloh National Military Park is located in Hardin County TN.
The only unit which qualifies is Crews' Tennessee Battalion:

http://www.tngenweb.org/civilwar/csainf/crews.html

This command served in Trabue's Brigade of Breckinridge's Corps at Shiloh. Trabue's report mentions that the battalion behaved well and was assigned to take prisoners back to Corinth MS.

There were other companies from Hardin County that may have been more colorful, such as Capt. C. S. Robertson's "Hardin County Yankee Hunters", but they were not involved in this battle.