The militia was required to have a musket, ball, powder and a bayonet equivalent to that used for military service and to drill with same. The rationale that the people would be armed with the same arms as a regular army troop means that what they had they not only could have but should have.
Off the top of my head I am thinking that was the second militia act of 1792 but don't take my old memory's word for it.
This, of course, post dated the Bill of Rights and the 2nd amendment of 1791 with the two militia acts of 1792 (OMG, imposing regulations on the 2A!) which were made permanent in 1795 (because of expiration), but then amended in 1862, and finally replaced by the Militia Act of 1903 that set up the National Guard.