Rummel and Shipman were two of three candidates who ran to fill the Frisco City Council Place 5 seat vacated by Dan Stricklin, who resigned to run for the Denton County Commissioners Court.
Rummel finished first with 46 percent of the vote. Shipman received 41 percent.
Candidates must break 50 percent to win.
Third-place finisher Sai Krishna drew 13 percent.
A total of 5,098 voters cast ballots in the special election—a turnout of just 4.1 percent of the city’s eligible voters.
A runoff is scheduled for March 26.
The winner will serve the remainder of Stricklin’s term, which runs through May 2023.
Krishna said he plans to run again in the regular May city council election. The candidate filing period ends February 18.
Special election results are posted on the city of Frisco’s website.