Indiana's voter turnout was much lower than the previous presidential primary four years ago.
Four election staff members have been accused of forging signatures on Democratic ballots in 2008.
The Democratic gubernatorial candidate says eliminating the tax would attract businesses to the state.
Senator Dick Lugar conceded to Richard Mourdock in a primary-night speech Tuesday.
Five Democratic candidates are running in the 9th district primary.
The 2nd district seat is open since Joe Donnelly is running for Senate.
8th District Congressman Larry Bucshon has raised substantially more money than his Republican opponent Kristi Risk.
Senator Dick Lugar faces a tough challenge in the GOP primary there on Tuesday from the state's treasurer, who is running to his right.
U.S. Congressman Mike Pence is running for governor, meaning there is no incumbent in the 6th district race.
A poll by a Republican and Democratic pollster shows Richard Mourdock with a large lead over incumbent Senator Richard Lugar.