South Dakota lies in both the Mountain Time Zone and the Central Time Zone. Mountain Time contains most of the western half of the state, including Mount Rushmore. Rapid City is the largest city in the Mountain Time portion of the state. Central Time contains the eastern half of the state, including the state capital, Pierre, and the largest city, Sioux Falls.
The 2 zones for South Dakota as given by zone.tab of the IANA time zone database. Columns marked * are from the zone.tab.