Fully 16 percent of wealthy women are undecided – twice the percentage of undecideds for all American voters.
Affluent women, in fact, are more likely to vote for Mitt than affluent men, about 46 percent of whom plan to vote Romney.
Ron Kurtz, president of the Affluence Research Center, said that affluent women voters tend to focus on economic issues like jobs, the economic recovery and the deficit more than other women. And they see Romney as a better candidate to address those issues. (Read more: Do Tax Crackdowns on the Wealthy Pay Off?)
“The issues related to the economy and deficit are more important, relatively speaking, to these women,” he said.
Overall, affluent voters are still leaning toward Romney. The poll showed that, in total, 48 percent of the affluent plan to vote for Romney while 35 percent plan to vote for Obama. Sixteen percent of all affluent voters are undecided.
The top five issues for these voters in the poll were “plans for the economic recovery,” “balancing the federal budget,” “reducing federal debt,” and “plans to create new jobs.” Income taxes came in fifth place among top issues. (Read more: Only the Mega-Rich Got Richer)
Kurtz said that, while it’s not surprising that Romney leads among the affluent, “I was a little surprised he didn’t do better. He still doesn’t have half of this vote.”
The large number of undecideds, he said, suggest that the wealthy are still waiting for more specifics from both candidates on their plans for the economy and federal spending.
“I think the debates will be very important for this group,” he said. “These are discriminating, careful voters and they’re waiting for more details.”
-By CNBC's Robert Frank
Follow Robert Frank on Twitter: @robtfrank