The British P1853 Enfield Rifled Musket was a .57 caliber weapon. Over 500,000 of these weapons were imported to the South through the blockade, and a little bit more than that to Northern ports. They would NOT have used a round ball.
As to round balls being used in the M1855, M1861 or M1863 Rifled Musket (Generically called "Springfield's), there is absolutely NO evidence to support this. Federal troops were issued standardized ammunition, so the likelihood of a Union solider using a round ball in a rifled musket is practically non-existent. Equally so for Confederate troops. Confederates used machinery captured at the Harpers Ferry Arsenal to manufacture there own version of the M1855 rifle (First pattern was the "high-hump rifle, omitting the Maynard priming door on the lock). This rifle, manufactured at the Richmond Arsenal, and so named - the "Richmond Rifle" also shot a conical ball. The Confederate forces had a WIDE variety of conical ammunition at their disposal, up to and including captured Federal ammunition.
"IF" this ball is Civil War related, it is probably from a Union or Confederate secondary rifle. Though the imported Lorenz musket is most commonly seen in .54 caliber, there were some that were imported in .58 smoothbore. There is also the possibility that this could be a Confederate non-standard ball, as used in a hunting style rifle.
Other possibilities would include:
A ball from an earlier war
OR:
Who is to say that it is military. Though it is in a military caliber, it could very well be a hunting ball.