The birth record for unnamed son born to William Todd and Mary Senior Todd [sic] 20 Dec 1880 belongs to Charles, based on son's ages in subsequent census records.
"New York, New York City Births, 1846-1909," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:271J-1JC : 11 February 2018), William Todd in entry for Todd, 20 Dec 1880; citing Manhattan, New York, New York, United States, reference cn 301206 New York Municipal Archives, New York; FHL microfilm 1,322,159.
"United States Census, 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MSV4-Q6G : accessed 7 November 2018), Charles R Todd in household of Scle*Ft Todd, Borough of Manhattan, Election District 7 New York City Ward 11, New York County, New York, United States; citing enumeration district (ED) 256, sheet 18B, family 408, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, 1972.); FHL microfilm 1,241,092.
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It may be possible to confirm family relationships with Charles by comparing test results with other carriers of his ancestors' Y-chromosome or mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Charles: