Except for newly-qualifying parties, Idaho technically provides for a primary for all ballot-qualified parties. However, no primary is held when only one candidate files in any particular party’s primary for any particular office.
But, there will be a Constitution Party primary ballot printed up for the May 20, 2014 primary in the First Legislative district. That is because two candidates filed for the party’s nomination for State Senate. They are Christian Fioravanti and Jack Mervin. As far as is known, this is the first primary held for any party, other than the Republican and Democratic Parties, in Idaho, in decades. See this story.
The Constitution Party had the option late last year to notify the state that it wants to open its primary to independent voters, a step the Democratic Party took. But the Constitution Party did not exercise its option to tell the state that it wants independents to be able to vote in its primary, so the Constitution nomination will be settled by the party’s registered voters who live in that district.