Here's a quick, down-and-dirty summary of arms issued and/or transferred to Ohio and the state's attempts to maintain accountability.
Congress’ Militia Act of 1808 appropriated $200,000 annually to provide muskets to the states’ militia. The War Department initially apportioned the number given to each state based upon the number of enrolled militia and later upon Congressional representation, sufficient to arm one-tenth of the number reported. States could request various other arms besides muskets. Once delivered to the state, the weapons became state property and it was the state’s responsibility to maintain and safeguard the weapons thus issued. From 1808 through 1860, Ohio received almost 28,000 muskets and 7,000 rifles. Unfortunately, the state legislature failed to appropriate money for armories or require company commanders to post bond for weapons issued. Consequently, many weapons disappeared. As of 15 April 1861, the state Quartermaster General had either in the state arsenal or in the hands of the militia 2,767 muskets of all classes (to include approximately 600, .58 caliber muskets), 406 rifles, and 76 musketoons. The state collected 1,326 additional muskets and rifles from across the state. By the end of 1861, the federal government issued an additional 58,566 muskets and rifles of both foreign and domestic manufacture to arm the Ohio volunteers. Once a regiment mustered into federal service, though, the weapons passed out of state ownership and control.
Dennison’s state of the state address in January 1862 reminded the legislature of the “impoverished condition” of the state in regard to arms in April 1861 and, because the federal government had assumed control of the arms issued to volunteers, lamented the fact that the state had no more arms than it had when the war broke out. Dennison and his successors were keenly aware of the need for arms with which to equip the home defense force. Kirby Smith’s siege of Cincinnati in 1862, Morgan’s Raid in 1863, and Clement Vallandingham's pro-southern activities in the state proved the validity of the governors’ concerns. Under the auspices of the 1808 Militia Act, the federal government in September 1863 transferred to Ohio about 27,000 second and third class muskets, of both U.S. and foreign manufacture. Among the different models transferred were .54 caliber U.S. rifles, light French rifles, U.S. .69 caliber M1816/22 and M1842 muskets, both rifled and smoothbore; Austrian rifle muskets in .54 and .58 caliber; .71 caliber French rifle muskets; .70 and .71 Prussian and Saxony muskets; and 400 Jaeger rifles. The value of these arms amounted to $188,589.50. Many of these weapons were subsequently issued to the newly re-organized Ohio Volunteer Militia, renamed the National Guard in 1864.
Ohio partially solved its historic problem of maintaining accountability of its weapons in 1863. In that year, state law required company commanders to post bond for the weapons issued to their companies. That same year, the federal government vacated the jointly occupied arsenal in Columbus thus freeing up a secure storage space for the weapons transferred to Ohio, but not yet issued to a unit. These measures were partially successful, but company commanders were reluctant to post bond on weapons that they could neither secure nor account for once given to a soldier. To help maintain control of its public property, the state die-stamped OHIO. (note period) on its arms and equipment to show public ownership. Ohio placed its stamp on the stock in at least one, and sometimes two places: the wrist and the flat. The stamps were of two sizes . The larger size left a wide, deep impression in the wood and was generally followed by a period. This marking appears on the M1841 rifle, M1842 musket, and the M1861 rifle musket, among others. The smaller stamp, with thinner lettering, is found on the wrist of M1842 pistols, some French muskets, and a few leather goods.
By the way, the Ordnance Department had briefly tried something similar in 1830 when it stamped the state’s name on the barrels of arms issued under the 1808 Militia Act. The Department soon suspended the effort because of cost and other concerns.
Marking the muskets continued through at least the end of the war. M1861 rifled muskets occasionally appear on the collector circuit with the Ohio mark as do some one-offs: a Wesson carbine (small stamp) and a Swiss rifled musket, for example. Once the state received serial numbered trapdoors, there was no longer a need to mark the weapons.