The state of Ohio did not keep birth or death records prior to 1856 or 57. It just was not done. If you are in the Chillicothe area you might check out the Genealogical Section at the Chillicothe Library on Paint Street or the Ross County Genealogical Society on Douglas Avenue. Deerfield Township Cemeteries were enumerated many years ago and if a tombstone existed it would be recorded in the book. There are also a couple Histories of Deerfield Township books at those places. If died after 1856 and was still in Ross County, the death record may be found there also, but if an adult only age, cause of death and township. Good Luck.