Florida Gov. Charlie Crist (I) leads his Republican and Democratic challengers in the state's Senate race, according to a Quinnipiac poll released Wednesday.

Crist — who left the Republican Party in late April after trailing Marco Rubio in the GOP primary — leads the former Florida House Speaker 37 percent to 33. Rep. Kendrick Meek, the Democratic front-runner, took 17 percent.

The poll was released after former Republican Party of Florida Chairman Jim Greer was charged with defrauding the party of over $100,000.

When he was a Republican, Crist hand-picked Greer to run the party, and some thought the charges could come back to bite the governor. Florida law enforcement dropped the charges June 2. The poll was taken June 1-7.

Crist also has strong support among independent voters in the swing state; 51 percent of them support him, compared to 26 percent who back Rubio and 10 percent who back Meek. Rubio has the strong support of Republicans, with 64 percent backing him and 28 percent backing Crist.

“Gov. Charlie Crist leads Marco Rubio by a nose in the Senate race. Obviously, there is a long time until November, but the governor is doing very well among independent voters [and] almost as well among Democrats as Meek," Peter A. Brown, a Quinnipiac polling official, said in a statement. "With Rubio getting two-thirds of the Republican vote, the fate of Gov. Crist, who switched from a Republican to independent six weeks ago, depends heavily on his ability to appeal to Democratic voters."

Democrats favor Meek, but less so than Republicans back Rubio. Forty-four percent support Meek while 34 percent support Crist, who has hired several Democrats to work on his campaign. Meek also faces a primary challenge from billionaire businessman Jeff Greene.

A poll released late last month also showed Crist leading Rubio and Meek 30-27-15, but that was taken before Greer was charged.

Quinnipiac surveyed 1,133 Florida voters and the poll has a margin of error of 2.9 percent.