According to the Genealogical Record of the Barnum Family, he served from August 11, 1862 until June 12, 1865 as a soldier in Company "K", 103rd Regiment, Ohio Volunteer Infantry. According to Veterans Administration records, he received a pension as an Army Invalid and his widow Sarah received a pension as an Army Widow.
His obituary says he was born of Scotch-Irish stock. The Barnum line of descent is purely English, so the reference was possibly to his mother's side of the family. He was a carpenter and upholsterer.
In the 1900 US Census for Medina Village, Township and County, Ohio the family of Richmond Barnum was enumerated as follows:
Dwelling #280; Family #280
Barnum, Richmond S.; Head; W; M; b. Jan 1833; 67; M; married 46 years; b. NY; father b. Canada; mother b. NY; Cabinet Maker; employed full year; can read, write and speak English; Owns home with mortgage
Barnum, Sarah C.; Wife; W; F; b. Feb 1837; 63; M; marreid 46 years; mother of 5 children; 4 living; b. OH; father b. CT; mother b. CT; can read, write and speak English
His obituary and Ohio Death Record give his birth place as New York,
while certain LDS records show it as Danbury, Fairfield, Connecticut.