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MIAMI (CBSMiami/NSF) – Democrat Hillary Clinton holds slight edges over Republicans Marco Rubio and Jeb Bush in potential 2016 presidential battles in Florida, but voters are concerned about the honesty and trustworthiness of the former secretary of state, a new poll shows.

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The poll, released Wednesday by Quinnipiac University, said Clinton leads Rubio, a Florida senator, by a margin of 47 percent to 44 percent in the critical swing state. She leads Bush, a former Florida governor who formally announced his presidential campaign this week, by a margin of 46 percent to 42 percent.

The margin of error in the poll of 1,147 Florida voters was 3 percentage points.

Quinnipiac also surveyed voters in Ohio and Pennsylvania, two other closely watched swing states. Peter A. Brown, assistant director of the Quinnipiac Poll, said that perhaps the most troubling issue for Clinton “is how she is perceived by voters who continue to say she is not honest and trustworthy.”

In Florida, 43 percent of voters said they think Clinton is honest and trustworthy, while 51 percent said they do not, according to the poll. Those numbers were slightly worse for Clinton in Ohio and Pennsylvania.

But other than the close margins with Rubio and Bush, Clinton holds substantial leads over other potential Republican candidates in Florida. Clinton leads U.S. Sen. Rand Paul, R-Ky., by a margin of 46 percent to 39 percent in the state and tops other GOP presidential hopefuls by double digits.

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As Clinton seeks to become the first female president, her support in Florida has been buoyed by women voters, Brown said in prepared remarks accompanying the poll.

“The margin (against Rubio and Bush) stems from her ability to keep the gender gap running in her favor,” Brown said. “She holds low double digit leads among women when matched against either man and that is enough to make the difference.”

The poll was conducted from June 4 to Monday, which was the day Bush announced his candidacy during a heavily publicized event in Kendall. The Connecticut-based Quinnipiac frequently conducts polls in Florida and other states.

As a whole, Republicans ran better against Clinton in Ohio and Pennsylvania than they did in Florida. Also, Brown said the poll results show that Rubio has a “tiny edge” over the Republican field in the three states.

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The News Service of Florida’s Jim Saunders contributed to this report.