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Shan Tsutsui has a 12 percentage point lead over Clayton Hee in the Democratic lieutenant governor primary, according to a new Civil Beat Poll.

Tsutsui, the incumbent, has 41 percent of the vote while Hee, a state senator, has 29 percent. But 29 percent of likely Democratic primary voters are unsure who they’ll vote for.

Civil Beat surveyed 1,078 registered Hawaii voters statewide June 7-9Ìýfor the lieutenant governor’sÌýrace. Of those, 729 said they expected to vote Democrat in the Aug. 9 primary.

The poll, conducted by , included a mix of landline and cell phone users and has a 3.6 percent margin of error.Ìý

We did not poll three other Democrats running for LG, including candidate Mary Zanakis, a former television reporter.

On Thursday, we published our results on the governor’s race, which shows incumbent Neil Abercrombie trailing state Sen. David Ige 48 percent to 37 percent.

While sitting Democratic governors in Hawaii have sometimes received spirited challenges from within the party, it’s unusual to have a contested primary against a sitting lieutenant governor.Ìý

But it’s also unusual in that Tsutsui is an appointed LG, having accepted the position in December 2012 when Abercrombie namedÌýBrian Schatz to the U.S. Senate.

Depending on what happens in the primary, the Democratic ticket for the general election could include the two incumbents, the two challengers or one of each.

Whatever the ticket’s composition, the Democrats will oppose a Hawaii Independent PartyÌýticket headed by Mufi Hannemann, the former Honolulu mayor, and his running mate Les Chang, a former Honolulu city official.

The Republican ticket will likely be led by Duke Aiona, the former lieutenant governor, and either Pastor Elwin Ahu or businessman Warner “Kimo” Sutton.

Hee, who wants to make the LG job more influential, feels the seat is up for grabs. When he announced his candidacy last month, he said his own internal polling suggested he would do well in the race.

Hee is a high-profile politician and has been in the headlines a lot. Just this week, he called on Abercrombie to show leadership and fix the troubled Hawaii State Hospital.

Hee and other senators have been conducting an investigation intoÌýhigh rates of patient assaults on staff as well as allegations of mismanagement, overtime abuse and nepotism.

But HeeÌýis also a controversial figure who has rubbed someÌýthe wrong way.Ìý

The Democratic ticket for the general election could include the two incumbents, the two challengers or one of each.

By contrast, Tsutsui has a more easygoing personality. But he is largely unknown outside of his home island of Maui and the Hawaii Legislature, where he was once Senate president.

To change that, Tsutsui’s campaign recently aired two television commercials to reintroduce himself to voters.

Ìý• Stay plugged in to campaigns and candidates this election season with Civil Beat’s Hawaii Elections Guide 2014, your source for information on federal, state and local elections.