The majority of the papers of Dr. Samuel H. Stout are located at the University of Texas at Austin, however, for the story on the dispersion can be found in "Confederate Hospitals on the Move: Samuel H. Stour and the Army of Tennessee" by Glenna R. Schroeder-Lein.
Below is a link to the description of the collection in Texas. I have extracted the information on the Dalton Hospitals but further down the description on the link you will find some microfilm rolls that may be of interests. This stuff did not make into the National Archive collections in the postbellum period and I have found a number of men in them that the information is not reflected in the Compiled Service Records. Researchers have not begun to scratch the service of this material. Jack D. Walsh's book "Two Confederate Hospitals and their Patients, Atlanta to Opelika" with its companion CD begins to tell the tale of Fairground Hospitals No. 1 and No. 2. He used the material out Stout's records that are all over the country right now.
http://www.lib.utexas.edu/taro/utcah/00042/cah-00042.html
I hope this helps.
Respectfully,
Gerald D. Hodge, Jr.
M.A. Military History - Civil War Concentration.
War Between the States Historian
Historian: 39th Georgia Volunteer Infantry Regiment
Descriptive Summary
Creator: Stout, Samuel Hollingsworth
Title Samuel Hollingsworth Stout Papers,
Dates: 1837-1902 (1860-1865)
Abstract Primarily Confederate States of America Army medical records relating to hospitals under the command of Samuel Hollingsworth Stout, Confederate Medical Director of Hospitals, Army of Tennessee. Includes essays written by Stout's daughter, Katherine Stout Moore.
OCLC Record No. 34197007
Extent 22 ft., 4 in., papers 14 reels, microfilm
Language English.
Repository Center for American History, The University of Texas at Austin
Papers
box 2G390
Dalton, Georgia:
Asylum Hospital, J. B. Murfree, surgeon
Cannon Hospital, D. W. Morrison, surgeon
Law Hospital, Alexander Erskine, surgeon
Oliver Hospital, Thomas F. Lee, surgeon
Headquarters reports
Receiving and Distribution Hospital, R. P. Bateman, surgeon
St. Mary's Hospital, J. S. McCain, surgeon
Stout Hospital, Lunsfotte Yandell, surgeon
All hospitals, W. L. McAllister, surgeon in charge
Oversized Documents
box 2.325/AA36
Dalton, Georgia
Asylum Hospital, J.B. Murfree, surgeon
Cannon Hospital, D.W. Morrison, surgeon
Law Hospital, Alexander Erskine, surgeon
Oliver Hospital, Thomas F. Lee, surgeon
Receiving and Distributing Hospital, R.P. Bateman, surgeon
box 2.325/OD18 (M3) Receiving and Distributing Hospital
box 2.325/AA36 St. Mary’s Hospital, J.S. McCain, surgeon
Stout Hospital, Lunsfotte Yandell, surgeon
All hospitals, W.L. McAllister, surgeon in charge