Fred Thompson is tied with Rudy Giuliani among state Republicans.
According to a June survey by the conservative Civitas Institute, the former Tennessee senator and the former New York City mayor were neck and neck at 24 percent.
Sen. John McCain came in third, with 16 percent, while former Massachusetts Gov. Mitt Romney came in last, with 6 percent.
A previous survey by a Democratic firm showed Thompson with a more commanding lead.
The poll also showed former Sen. John Edwards in the lead among Democrats at 25 percent, followed by Sen. Hillary Clinton at 20 percent and Sen. Barack Obama at 18 percent.
The survey of 800 active voters was conducted June 13-15. It has a margin of error of 3.7 percent.
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