While it is true no file exists for Col. Polk, he is listed in the Compiled Service Records with the Field and Staff in the introductory Unit Information section at the beginning of the file.

Unit Information:

"Cocke's, formerly Hawthorn's, formerly Johnson's Reg. Ark. Inf., also called 39th Regt.

Johnson's Reg. Ark. Inf.

A. W. Johnson, Col., Resigned Nov. 6, 1862
D. W. Ringo,, Lt. Col., Resigned Nov. 7, 1862

Hawthorn's Reg/. aft/Polk's Ark. Inf.

A. J. Hawthorn, Col., Brig. Gen. Jan. 5, 1864
Cadwallader Polk, Lt. Col., Col.
John B. Cocke, Major, Col., Killed Apr. 30, 1864
Jacob C. Molea, Lt. Col."

M317: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Arkansas,
Roll 242: 62nd Militia, Adams' Infantry, Borland's Infantry, Cocke's Infantry A-B