Concur with UCVRelics. By the vision of the unusual shape, it appears to be a dimick rifle bullet.
The relevant entry for a 'dimick' in 'A Handbook of Civil War Bullets & Cartridges' (at page 72) by Thomas & Thomas says,
...'These are found in almost every diameter from .36 to .69 caliber. They feature numerous teat sizes and even cone cavities.'...
I assume the Dimick bullet was developed for the Dimick rifle. Horace E. Dimick originally came from Vermont. He was in Covington Kentucky in 1848 when he lost a shooting match to Hiram Berdan. He later moved to St. Louis, MO, where he made target rifles and plains rifles. When the war started he formed a group for the western theater like Berdan's in the east. See the link below:
..."These bullets (the ones displayed) are made from moulds made by or for Horace E. Dimick of St. Louis, MO. The moulds were issued along with the Dimick American Deer and Target Rifles to 'Birge's Western Sharpshooters' in 1861 and 1862. The Western Sharpshooters eventually became the 66th. Illinois Infantry."...