Correction: A previous version of this article incorrectly said that Meg Whitman served as vice president of Bain Capital. She was a vice president at Bain & Co., a separate entity. This version has been corrected.

It was a memorable anecdote, one that could have shown Mitt Romney’s sensitivity toward the issue of gender equality in the workforce.

The Republican presidential candidate said he had reached out to a women’s group to find qualified female applicants for senior-level positions in his administration after he was elected governor of Massachusetts in 2002. He took the action, he said, after realizing that only men had applied for those jobs.

“I said: ‘Well, gosh, can’t we find some women that are also qualified?’ ” Romney said during Tuesday night’s presidential debate. “And so we took a concerted effort to go out and find women who had backgrounds that could be qualified to become members of our Cabinet. I went to a number of women’s groups and said, ‘Can you help us find folks?’ And they brought us whole binders full of women.”

Romney’s anecdote came in for intense scrutiny Wednesday after the Phoenix, a Boston-based publication, reported that the Massachusetts Women’s Political Caucus, the group that led the hiring initiative, had reached out first to Romney, not the other way around. The Phoenix also pointed out that the percentage of women who held senior-level positions actually declined at the end of Romney’s time in office.

According to a 2007 report from the caucus, the percentage of women in top positions stood at about 30 percent in Massachusetts just before Romney’s 2002 election. But it dropped to about 28 percent near the end of his administration. It rose to 34 percent eight months after Gov. Deval Patrick, a Democrat, took office in 2007.

Elizabeth Levine, who chaired the women’s caucus when Romney was elected, said this type of fluctuation is the norm. She said that administrations often appoint internal candidates to fill short-term positions near the end of a term and that women have a natural disadvantage in those situations. “If you don’t have a lot of new people in the pipeline, it’s harder to fill those positions with women,” she said.

But Jesse Mermell, former director of the caucus’s hiring initiative, known as MassGAP, blasted Romney for relying on the women’s group to find qualified women for top-level positions. “It’s shocking to me that after 25 years, a professional from the very highest levels of corporate America needed help with this,” she said.

Little is known about the number of female employees at Bain Capital, the private equity firm that Romney founded before entering politics. As a nonpublic company, it is not required to make such information available.

The Boston Globe reported that Bain had no female partners during Romney’s tenure. Still, one female hire proved beneficial to the firm’s reputation: Meg Whitman joined Bain as a consultant and rose to become senior vice president of Bain & Co. She went on to become chief executive of Hewlitt-Packard and win the 2010 Republican nomination for governor of California.

Levine did not criticize Romney for accepting help from MassGAP and the women’s caucus. “From my perspective, it’s a sign of strength to be able to reach out to groups and get names and good people who might make your group good,” she said.

The Massachusetts Women’s Political Caucus describes itself as nonpartisan. Founder Marge Schiller is a registered Democrat, and many of the groups leaders donate exclusively to Democratic campaigns. But some key members of the organization, including its former president and numerous board members, are prominent Republicans on the Massachusetts political scene. They include: former lieutenant governor Kerry Healy, a former board member who served as Romney’s liaison to the caucus; Ann Murphy, the organization’s former president; and Jennifer Nassour, a board member who was chairman of the Massachusetts Republican Party from 2009 until 2011.