Republican Party Chairman Kenneth Buelter said there were two discrepancies found during the March 13 canvassing of votes, but they did not alter the tie between the two candidates in the March 4 primary.
Bowman and Calhoun each received 489 votes in the election.
All registered voters except those who voted in the Democratic primary on March 4 are eligible to cast ballots in the county judge runoff.
Goliad County/District Clerk Mary Ellen Flores said early voting for the runoff will be held May 19-23 at the Courthouse Annex. Times will be announced this week.
Flores also said Buelter and Democratic Party Chairman Charles Clapsaddle would determine the polling places.
The winner between Bowman and Calhoun will face Democratic nominee Ernest Alaniz in the Nov. 4 general election.
The city elections will be held Saturday, May 10 at City Hall from 7 a.m. to 7 p.m. Early voting will be April 28-May 4 at City Hall from 9 a.m. to 5 p.m. Extended early voting will be May 5 and 6 at City Hall from 7 a.m. to 7 p.m.