In 1980, State Senator Thomas C. Kennedy declined to seek re-election.[2] Peterson ran to succeed him in the 21st district, which was based in Madison and Pierce counties.[3] In the nonpartisan primary, he faced businessman Paul McIntosh and former Madison County Judge R. Bruce Penning.[4] McIntosh narrowly placed first in the primary, receiving 37 percent of the vote to Peterson's 36 percent and Henning's 27 percent,[5] and McIntosh and Peterson advanced to the general election.[6] Peterson ultimately defeated McIntosh, winning 54 percent of the vote to McIntosh's 46 percent.[5][7]
Peterson ran for re-election to a second term in 1984.[8] He was challenged by J. R. Peterson, a state highway department engineer, and Steven Liewer, a carpenter.[9][10] Senator Peterson placed first in the primary by a wide margin, receiving 74 percent of the vote to J. R. Peterson's 17 percent and Liewer's 9 percent.[11] They advanced to the general election,[12] where Peterson won re-election, 75–25 percent.[11][13]
In 1988, Peterson ran for re-election to a third term.[14] He was challenged by J. R. Peterson, in a rematch of their 1984 campaign,[15] and stockbroker T. Patrick Stinson.[16] In the primary election, Senator Peterson placed first, receiving 56 percent of the vote to Stinson's 33 percent,[17] with Peterson and Stinson advancing to the general election.[18] In the general election, Peterson declined to debate Stinson, stating that he "ha[s] never felt debates proved anything," but Stinson attacked him for his refusal, arguing, "He knows that opening dialogue is going to cause him some grief."[19] Peterson ultimately defeated Stinson, winning re-election 59–41 percent.[17][20]
Following redistricting in 1992, the 21st district was originally abolished, and Peterson declined to seek re-election. On July 2, 1992, the Nebraska Supreme Court struck down the state's new redistricting plan,[21] resulting in the recreation of a Madison County-based district, numbered the 19th district.[22] Peterson did not revisit his decision to not seek re-election,[23] and was succeeded by Connie Day in the 19th district.[24]