The quick answer about the Ohio mark is that the state began marking its property after the Ordnance Department transferred about 27,000 second and third class muskets to Ohio in September 1863. Prior to that time, Ohio did not mark its public property and accountability was a huge issue. For example, between 1808 and 1860, the federal government issued Ohio 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. When the war began, the state could account for only 2,767 muskets and 406 rifles. Ohio was able to collect an additional 1,326 weapons from across the state, but they all went to arming the 3-month and 3-year volunteers. As the soldiers departed for the front, they took these weapons with them - which were now the property of the US government. When Governor Dennison gave his State of the State address in January 1862, he lamented the fact that Ohio had few weapons with which to defend its borders. The siege of Cincinnati, Clement Vallandigham and the copperheads, Morgan's raid, and the presence of two POW camps proved Dennison right. In September 1863, the government transferred second and third class US and foreign made muskets to the state with which to arm the National Guard. It was with this transfer that the state started marking its property; not only small arms, but leather goods as well. While the order directing this marking has yet to be found, the state arsenal listed in its 1863 inventory two OHIO. (note period) stamps. The markings continued until the 1870s when serial numbered weapons were issued to the state.
I realize that's not a really quick answer, but that's pretty much the gist of it.
I hope this helps.