Dyer's Compendium does not show this unit as a battalion, but as a regiment:
1st MISSISSIPPI REGIMENT MOUNTED RIFLES
Organized at Memphis, Tenn., March, 1864. Attached to District of Memphis, Tenn., 16th Army Corps, Dept. Tennessee, to June, 1864. 1st Brigade, Cavalry Division, District of West Tennessee, to July, 1864. 1st Brigade, 2nd Cavalry Division, District West Tennessee, to December, 1864. 1st Brigade, Cavalry Division, District West Tennessee, to June, 1865.
SERVICE - Duty in the Defences of Memphis, Tenn., till August, 1864. Expedition from Memphis to Grand Gulf, Miss., July 7-24. Near Bolivar July 6. Port Gibson July 14. Grand Gulf July 16. Smith's Expedition to Oxford, Miss., August 1-31. Tallahatchie River August 7-9. Hurricane Creek August 9. Oxford August 9 and 11. Hurricane Creek August 13-14 and 19. At Memphis and in District of West Tennessee, till December. Grierson's Expedition from Memphis against Mobile & Ohio Railroad December 21, 1864, to January 5, 1865. Verona December 25, 1864. Okolona December 27. Egypt Station December 28. Franklin and Lexington January 2, 1865. Mechanicsburg January 3. The Ponds January 4. Moved from Vicksburg to Memphis and duty there till June, 1865. Expedition from Memphis into Southeast Arkansas and Northeast Louisiana January 26-February 11. Mustered out June 26, 1865.
Source: A Compendium of the War of the Rebellion - Frederick H. Dyer, 1908