If you go to familysearch.organd enter Harriet Peck of Connecticut with her birthdate, here are some examples of persons with that name in the US Census.
Harriet Peck United States Census, 1850 birth: 1798 Connecticut residence: 1850 Troy,? Ashland,? Ohio,? United States Harriet Peck United States Census, 1860 birth: 1797 Conn residence: 1860 ,? Litchfield,? Connecticut Harriet Peck United States Census, 1850 birth: 1799 Connecticut residence: 1850 Litchfield,? Litchfield,? Connecticut,? United States William H Peck United States Census, 1850 birth: 1797 Connecticut residence: 1850 Ossining,? Westchester,? New York,? United States
From the 1870 US Census, her is Harriet Peck of CT in OH name: Harriet Peck estimated birth year: 1798 gender: Female age in 1870: 72y color (white, black, mulatto, chinese, indian): White birthplace: Connecticut home in 1870: Ohio, United States
Household Gender Age Birthplace Chancey F Peck M 44y New York Mary Peck F 40y Connecticut Sanford Peck M 17y Ohio Blinn Peck M 11y Ohio Elwin Peck M 6y Ohio Frank Peck M 3y Ohio Harriet Peck F 72y Connecticut
From the 1880 US Census, here is Harriet Peck of New London living in Ohio at the age of 82.
name: Harriet Peck residence: New London, Huron, Ohio birthdate: 1798 birthplace: Connecticut, United States relationship to head: Self spouse's name: spouse's birthplace: father's name: father's birthplace: Connecticut, United States mother's name: mother's birthplace: Connecticut, United States race or color (expanded): White ethnicity (standardized): American gender: Female martial status: Widowed age (expanded): 82 years occupation: At Home nara film number: T9-1035 page: 140 page character: D entry number: 2776 film number: 1255035