MDAH has this history in its collections, looks to be a good starting point.
Author: Jarman, R.A.(Robert A.)
Title: The history of Company K, 27th Mississippi Infantry and its first and last muster rolls / by R.A. Jarman.
Imprint: Aberdeen, Miss. : Aberdeen Examiner, .
Local Call Number: 973.7462/J37h
In-house Request: Archival Reading Room
Descr. 53 leaves : port. ; 28 x 22 cm.
Gen. Note: Photocopy.