Heath, a state representative from Mayfield, lost to fellow state representative Ryan Quarles by 1,427 votes out of the more than 183,000 cast in the race. The two men are vying to succeed Republican James Comer, who did not seek re-election in order to run for governor.
Comer trails Republican Matt Bevin by 83 votes after Tuesday's primary. He has also requested a recanvass, or a review of the state's voting machines and absentee ballots. State law requires the recanvass for both races to begin at 9 am on May 28.
The review includes every precinct in the state's 120 counties.