Please post a picture of the back and give us a size. And, while I know very little about rosettes I did a search and found that these are or were reproduced by the Hanover Brass Company. Look almost to the bottom of the page in this link.
Beautiful CS rosette. One was dug on Hansborough Ridge in 2007 at a DIV hunt. They aren't found often but if you are in Richmond the odds are obviously better. Banner find in my book.
OK, as not many are found in CW context, can we assume its another case of Civvy objects in battle situations? Or was it part of the Military Horse Dress?