Donald Trump Donald John TrumpUS reimposes UN sanctions on Iran amid increasing tensions Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally MORE only holds a slim lead over Hillary Clinton Hillary Diane Rodham ClintonJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Momentum growing among Republicans for Supreme Court vote before Election Day Warning signs flash for Lindsey Graham in South Carolina MORE in a three-way match-up in Utah, suggesting the deep-red state could be in play during the general election.

Trump, the presumptive GOP presidential nominee, is supported by 29 percent of registered voters in Utah, according to a poll released this week from Florida-based Gravis Marketing, with Clinton, the Democratic front-runner, following closely at 26 percent.

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Libertarian nominee Gary Johnson takes 16 percent support in the poll, while another 29 percent opted for someone else. "I love Utah," Johnson tweeted, linking to the polling.

Utah hasn't gone to a Democratic presidential candidate since 1964, but voters in the state have shown strong reservations about Trump. The New York businessman placed last in the GOP primary there in March.

Mitt Romney, the GOP's last nominee, won his home state of Utah with more than 70 percent of the vote in 2012. He has been a leading voice among Republicans who say they won't vote for Trump or Clinton.

Without including Johnson, Trump bests Clinton in a hypothetical general election match-up by 7 points in the poll — 36 to 29 percent — with fully 35 percent of Utah voters, more than 1 in 3, opting for "other."

The survey of 1,519 registered voters was conducted May 31 through June 1 via telephone, with a margin of error of 2.5 percentage points.