• The Quartermaster General's office created 166,000 3x4 cards for soldiers who died between 1851 & 1903. These cards, arranged alphabetically, were microfilmed (M1845 - 22 rolls) and have since be digitized by Ancestry.com - see link below. The Ohio Genealogical Society is in the process of creating a database capturing all significant items included on the cards.
• Applications for Headstones in Private Cemeteries, 1909–1924 (entry 592)
• Applications for Headstones for Soldiers Buried at Soldiers' Homes, 1909–1923 (entry 591) - This includes burials in both state and federal Soldiers' Homes.
• Applications for Headstones 1925-1963 (entry 2110C) organized alphabetically in year groups 1925–1941, 1942–1948 then in groups of 2 or 3 years to 1963. The first set within this entry for the years 1925–41 has been reproduced as microfilm publication M1916, Applications for Headstones for U.S. Military Veterans, 1925–1941.
• Applications for Headstones 1964-1970 (entry 1942A)
• Interment Control Forms ca. 1928-1962 (entry 2110B) are arranged alphabetically by name of decedent so you would not need to know the date of the application.

• Mark C. Mollan, "Honoring our War Dead: The Evolution of the Government Policy on Headstones for Fallen Soldiers and Sailors"; Prologue, Spring 2003, Vol. 35, No. 1
• Trevor K. Plante, "Headstones and Burials," Military Service Records at the National Archives (Reference Information Paper 109)
• Headstones Provided for Deceased Union Civil War Veterans, 1879-1903 at Ancestry.com

NOTICE TO APPLICANT.
Write plainly and be careful to spell correctly the names of soldiers or other persons for whose graves headstones are desired; if any of them served under an assumed name, both the true name and the alias must be given.
Write the first or given name in full if known, as Chas. T. Jones instead of C. T. Jones.
Where soldier served with State troops, the State and arm of service (whether infantry, cavalry, or artillery) should be given; and in the case of a sailor or marine, the name of one or more vessels on which he served, and the approximate date of enlistment is required. The approximate dates of enlistment and discharge should also be given where the soldier served in the Regular Army.
By carefully observing these directions and giving the information called for in each column, delay will be avoided.
Officers or Committees of G.A.R. Posts and other persons having charge of securing headstones for soldiers buried in their vicinity should ascertain before ordering headstones whether or not the relatives or friends of the soldiers desire the headstones or whether they intend to erect private monuments.
Applications for headstone, the receipt of which have been once acknowledged by this office, should not be duplicated; the headstones will be furnished as soon as practicable.

NOTE.
Upon application to the Quartermaster General, U. S. Army, headstones will be furnished for unmarked graves of soldiers, sailors, and marines who served in the Army or Navy of the United States during any war or insurrection (including the Revolution), whether regular or volunteer, and whether they died in the service or since their muster out or discharge there from. Headstones will be furnished also for the unmarked graves of Army Nurses who had regular or volunteer commissions as such.
These headstones are of best American white marble, 39 inches long, 12 inches wide, and 4 inches thick, the top slightly rounded, and the portion of the stone which will be above ground when set is sand-rubbed; each headstone is inscribed with the name, rank (if above private), company, and State regiment, or other organization, to which the deceased belonged, cut in relief within a sunken shield. No deviation can be made from these specifications, which are prescribed by the Secretary of War, and the law does not provide for any expenditure for fences or for any other purpose except for the headstone as above described.
No money allowance is made in lieu of furnishing headstones.
Headstones will be shipped, freight prepaid by the Government, only to the nearest railroad station or steamboat landing; they will not be delivered to street addresses or to the cemetery.

MEMORANDUM.
Applicants must answer advisedly the following questions before stones can be furnished:
1. Are the headstones ordered at the request of the relatives in each case?
2. Is there a private monument or headstone at the grave (or graves)?
3. Do any of the relatives or friends intend to erect private monuments or headstones in the future?