Although you didn't mention her, the informant on William H. Smith's death cert must have been his daughter. Her name on the cert is Mrs. Perry Van Hoover, Chillicothe, Ohio.
Perry Van Hoover and family are in Kinnikinnick, Green Twp., Ross County, OH on the 1940 census:
head Perry 35 bp Tennessee, wife Odessa 29 bp Nebraska, son Perry Jr. 12 bp Ohio, son Gerald 6 bp Ohio, *father-in-law William Smith 71 divorced bp Ohio.
Odessa is shown in the Ohio Death Index as being born 2 Apr 1911, died 1 Apr 2004, father's name SMITH, mother's maiden name HALL. If you want to persue this, contact the Chillicothe library, http://www.crcpl.org/history
and request a copy of Odessa's obituary.
PS. Odessa Smith is in the 1920 census in Columbus, Ohio. Father was William H., mother Mattie plus 4 more siblings.