Here's what is found in the Official Records concerning Hood's furlough program.
Taken from Series 1, Vol. XLV, Pt. 2

George Martin

CORINTH, MISS., January 3, 1865.
His Excellency PRESIDENT DAVIS,
Richmond, Va.:
I respectfully ask for authority to furlough the Trans-Mississippi troops of this army. Their effective strength at present does not much exceed 2,000, which could, I think, by this means be much increased; I think it of vital importance. Please answer. Lieut. Col. J. P. Johnson will explain to you the campaign in Tennessee, in addition to my dispatch to the Secretary of War from Spring Hill, Tenn., and from the Bainbridge crossing of the Tennessee.
J. B. HOOD,
General.
p. 757

WAR DEPARTMENT, C. S. A.,
Richmond, Va., January 8, 1864.
General BEAUREGARD, Selma:
Repress by all means the proposition to furlough the Trans-Mississippi troops; the suggestion merely is dangerous; compliance would probably be fatal; extinguish if possible, the idea.
J. A. SEDDON,
Secretary of War.
p. 770

WAR DEPARTMENT,
Richmond, Va., January 8, 1865.
General J. B. HOOD, Tupelo, Miss.:
The proposition to furlough the Trans-Mississippi troops cannot be entertained; the suggestion is regarded as dangerous; compliance would probably be fatal; extinguish the thought in the troops, if practicable.
J. A. SEDDON,
Secretary of War
p. 770

TUPELO, MISS., January 11, 1865.
General G. T. BEAUREGARD,
Montgomery, Ala.:
I am very anxious to see you here in reference to the Trans-Mississippi troops, and also as to some system of furlough for other troops, and on other important matters.
J. B. HOOD,
General.
p. 778

TUPELO, January 16, 1865.
(Received 6.30 o'clock 17th.)
General SAM. COOPER:
To prevent disorder and desertion in Army of Tennessee. I have approved a judicious system of furlough. Copy of order will be forwarded for information of War Department.
G. T. BEAUREGARD.
p. 786

WEST POINT, January 16, 1865.
Col. E. J. HARVIE:
Captain Goodman, General Chalmers' adjutant-general, informs me that General Forrest ordered General Chalmers to furlough all West Tennesseeans for thirty days, dismounted Mississippians for fifteen days, and dismounted Alabamians for twenty days. I am having all such arrested, and Colonel Forrest, who is now here, is doing likewise.
POLLOK B. LEE,
Assistant Inspector-General, Army of Tennessee.
p. 786

HEADQUARTERS ARMY OF TENNESSEE,
Tupelo, Miss., January 16, 1865.
Lieutenant-General STEWART,
Commanding Corps:
GENERAL: If you have any troops in your command who live sufficiently near the present position of the army to justify, in your opinion, the granting them ten days' furlough, the same will be done and proper application made at once, provided the men go by organization, under officers, and pledge themselves to return at the expiration of the time. All obtaining such furloughs will be debarred the benefit of General Orders, No. 1, from army headquarters.
By command of General Hood:
A. P. MASON,
Lieutenant-Colonel and Assistant Adjutant-General.
(Same to Generals Cheatham and Stevenson.)
p. 788