The race has been caught up in controversies about the practice of "crossover voting," in which some outside groups are accusing Sen. Thad Cochran's (R-MS) campaign of encouraging Democrats and African-American voters to support him in the runoff.
The lawsuit, by Ronald W. Swindall, a supporter of Mississippi state Sen. Chris McDaniel (R) was filed on Monday. McDaniel is facing Cochran in the runoff for the GOP nomination for U.S. Senate.
In Mississippi, voters don't register by party in primaries. Mississippi state law prohibits people from voting in the Republican runoff if they voted in the Democracy primary on June 3.
Swindall filed the new lawsuit in chancery court in Jones County on Monday. It was dismissed by Chancery Judge Deborah Grambell on Tuesday according to the Associated Press.
Tea partiers who support McDaniel have been citing a Mississippi law that stipulates a voter can only vote in a party primary if the voter plans to back that primary's nominee in the general election. In 2008 a federal appeals court ruled that law as unenforceable.