Complex sentence: The non-partisan primary will be on Tuesday, June 5,2012; if no candidate receives a majority of primary votes, the top two vote-getters will appear on the ballot in the general election.
Split into simpler sentences: The non-partisan primary will be on Tuesday, June 5,2012. If a candidate receives a majority of primary votes, he or she will be declared elected; otherwise, the top two vote-getters will appear on the ballot in the general election.