The Texas Lyceum Poll released Wednesday also found many Texans aren't paying much attention to next year's elections yet.
The poll found Perry backed by 33 percent of those polled, while Hutchison had 21 percent. Some 45 percent of Texans were undecided.
The Perry celebrated the poll's findings, sending web links to the story from the campaigns Twitter page.
"After months of criticisms from Washington and tearing down Texas the Senator’s numbers continue to drop. Governor Perry will continue to talk about creating jobs, cutting taxes, protecting private property rights, and improving education." said Mark Miner, Texans for Rick Perry spokesman.
"To the extent this poll shows anything, it's that two-thirds of Texans don't want Rick Perry for yet another four years. His 39 percent support from 2006 is deteriorating. When Kay Bailey Hutchison begins laying out her vision for the state later this summer, we're confident that her substance will prevail over his rhetoric," said Hans Klingler, Texans for Kay Communications Director.
Debra Medina, another GOP candidate who didn't show up in the results, told NBCDFW.COM "With over 40% of potential Republican primary voters still undecided, according to the recently released Texas Lyceum Poll, it should be clear Texas Republicans are looking for an individual who will in fact, walk the talk...."
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On the Democratic side, 80 percent of those polled were undecided, but humorist Kinky Friedman had 10 perecent, followed by former ambassador Tom Schieffer, who was expected to announce his candidacy Wednesday, with 6 percent.
The poll had a margin of error of 3 percentage points.