Three states hold primaries on May 6: Indiana, North Carolina, and Ohio. They are the first primaries this year, other than the Illinois, Texas and District of Columbia primaries.
Both North Carolina and Ohio are holding primaries for more than just two parties. In North Carolina, the Libertarian Party has a contested primary for U.S. Senate. Any registered Libertarian, and any registered independent, can vote in that primary. The two major parties in North Carolina also let independent voters vote in their primaries.
The only other time North Carolina held a primary for the Libertarian Party was in 2012, when the party had a contested presidential primary. Almost 8,000 voters voted in the Libertarian 2012 primary.
Ohio is holding statwide primaries for the Libertarian Party and the Green Party, and primaries in certain parts of the state for the Constitution Party and the Socialist Party. No minor party in Ohio has any statewide candidates on its primary ballot, but the Green and Libertarian Parties have declared write-in candidates for some of the statewide offices: Governor for the Greens, and Secretary of State and Auditor for the Libertarians. Statewide candidates of the minor parties must poll 500 write-ins, in order to advance to November.
Although the Indiana Libertarian Party is ballot-qualified, it nominates by convention, not by primary.
Both Indiana and Ohio have open primaries. The voter registration forms in those two states do not ask voters to indicate partisan affiliation.