Kenneth,
I do not know of any detachments from the 11th/17th Arkansas which were attached to the 38th MS Mounted Infantry. The 38th was a part of Colonel Hinchie P. Mabry's Brigade on loan from Brigadier General Wirt Adams in Jackson. Mabry wrote an after action report but does not mention the 11th/17th, nor does division commander Abraham Buford or General Forrest. There are no officers of the 11th/17th mentioned in the list of officers killed in the battle. Dunbar Rowland's Military History of Mississippi notes that the 38th took the highest number of casualties in the brigade during the fight at Harrisburg but makes no mention of a detachment of the 11th/17th Arkansas. He also notes "all the regimental officers of the brigade" were killed or wounded.
Though I can find no mention in the OR or Crutes, I believe the 11th/17th were left behind with Wirt Adams and participated in the campaign against Major General Henry Slocum and his movement from Vicksburg toward the Pearl River. Adams did not write an after action report.
Tom