1880 - Name: Michael Barnett Age: 45 Birth Year: abt 1835 Birthplace: Ireland Home in 1880: Norwich, New London, Connecticut Race: White Gender: Male Relation to Head of House: Self (Head) Marital Status: Married Spouse's Name: Ellen Barnett Father's Birthplace: Ireland Mother's Birthplace: Ireland Occupation: Laborer
Michael Barnett 45, IRE - laborer Ellen Barnett 42, IRE Bartholemew Barnett 21, IRE - apprentice blacksmith John Barnett 18, IRE - works in cotton mill  Mary Barnett 16, IRE - works in cotton mill Dennis Barnett 14, IRE  Michael Barnett 10, IRE
You won't find his ancestory in the US census records.
Michael does not appear in the CT 1870 census.
TRY - Find a grave – FREE SITE - volunteer site all states; frequently has headstone pic DO NOT SEARCH FOR A MARRIED WOMAN USING HER MAIDEN NAME.