Parents were both born in New York per 1900 census record. Ron Hayward's compilation has mother Mary Green born in Indiana, and this matches the 1920 census record as well. Bible record for her indicates she passed at age 73; it's unclear if the birth year, death year, or bible age is incorrect.
Sources
"Iowa State Census, 1885," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/HCF2-13Z : accessed 12 Jan 2013), Caroline Theodosia Wiseman in household of James Dudley Wiseman, Cleveland, Davis, Iowa.
"United States Census, 1900," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/M9KM-5TM : accessed 12 Jan 2013), Theodosis Wiseman in household of James Wiseman, ED 27 Center Township Centerville city Ward 1-2, Appanoose, Iowa, United States; citing sheet 7A, family 152, NARA microfilm publication T623, FHL microfilm 1240416.
"United States Census, 1920," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/MDM4-1C9 : accessed 12 Jan 2013), Theodocia Wiseman in household of James D Wiseman, , Polk, Iowa; citing enumeration district (ED) , sheet 12B, family 285, NARA microfilm publication T625, FHL microfilm 1820509.
Hayward Family History compiled by Ron Hayward, references Norman W Cook bible and has photo of Theodosia.
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DNA Connections
It may be possible to confirm family relationships with Theodosia by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Theodosia: