His CSR contains a copy of his pardon/discharge on:

Card # 18

Andy Smith, Company D, 1st New Orleans Volunteers
Book mark: 4243-D-1884
War Department, Adjutant General’s Office
Washington, July 18, 1885
The charge of desertion of Feb.-May 16, 1866 against this man is removed and he is discharged to date February 16, 1866, under the provisions of the act of Congress, approved July 5,1884.
Discharge certificate furnished by Adjutant General’s Office July 28, 1865.

Compiled Service Records of Volunteer Union Soldiers Who Served in Organizations from the State Of Louisiana

Unfortunately, this document does not provide the reason his desertion charge was removed