Ingham County was established by an act of the Michigan Territorial Legislature on October 29, 1829, from portions of Shiawassee County, Washtenaw County and unorganized territory. It was attached for administrative purposes to Washtenaw County until 1838 when county government was established for Ingham.
The county was named for Samuel D. Ingham, the U.S. Secretary of the Treasury under President Andrew Jackson, making Ingham one of Michigan’s so-called Cabinet counties.
Source : Ingham County, Michigan wikipedia entry.
Also see History of County Creation.