I looked Catharine up in the cemetery book and it says "-14 Feb. 1805."
I see her in the 1900 census, which means it is at least 19xx.
I looked through the Death records for that time period (1900-1908) in Salem Twp. and I did not find a record for her.Most of the records for adults do not have parents listed, anyway.Ohio moved to death certs in late 1908.
There is a slight chance that the year is 1909, which would mean that there is a death cert.These would be in Columbus at the Ohio Historical Society.Perhaps you know the year with greater certainty.
I am not in a position to check the stone or at OHS.(I live out of state.)
The Tusc Co Gen Soc sells two obituary books for New Philadelphia in this time period.You might write to them and see if there is a listing.There is a small charge (ca. $5 plus copies).