Heath, a Bremen resident who is seeking re-election to a fifth Senate term, challenged Carruth on Friday to one debate in each of the three District 31 counties — Paulding, Polk and Haralson.
“My challenge of you is to meet me in front of the voters and present and defend any and all allegations,” Heath wrote to Carruth.
Carruth, former chairman of the Paulding County Commission and Georgia Department of Natural Resources board, responded he would not agree to the debates until Heath answered a state ethics complaint and commit to supporting a limit on lobbyist gifts to legislators.
The ethics complaint alleges Heath illegally received funds from a political action committee set up as an independent body that Heath helped establish to aid Republican Senate incumbents with primary election challengers.
Heath alleged Carruth did not meet residency requirements and owed the public money because of debts from a failed bank venture — charges later dismissed by an administrative law judge.
July 31 election results showed neither received enough votes to avoid the runoff. Heath received 45 percent and Carruth received 41 percent of the votes. J.K. Rogers of Dallas received 14 percent in the three-person race. More than 50.0 percent of votes are needed to win outright in a legislative race.
Meanwhile, former state representative Bob Snelling and Douglas County School Board member Mike Miller will square off Aug. 21 for the Republican nomination for State House District 66, which includes south Paulding and central Douglas counties.
Snelling, a House member from 1994 to 2002, received 49.63 percent of the vote, according to information from the Georgia Secretary of State.
Miller received 27.17 percent to finish second and qualify for the runoff. Former Douglasville mayor Mickey Thompson received 23.2 percent to finish third.
The runoff winner will face Democrat Kimberly Alexander of Dallas in the Nov. 6 general election. Alexander was unopposed for the Democratic nomination July 31.
However, incumbent District 19 State Rep. Paulette Braddock of Hiram easily won re-election in defeating Michael Ray James and Melissa Morrison in the Republican primary.
Braddock, who is seeking a second term, received 63 percent of the vote in defeating Morrison with 19 percent and James with 18 percent.
No Democrats qualified for the seat, making Braddock the de facto winner.
A total of 17,854 Paulding Countians, or 24 percent of registered voters, cast ballots in the primary.