WASHINGTON — More than a third of U.S. voters want to know more about Mitt Romney's tenure at the private equity firm Bain Capital and how much he paid in taxes, according to a poll released Tuesday.

The survey by the Pew Research Center also found that 41 percent of registered voters would like additional information about Romney's one term as governor of Massachusetts, where he signed health-care legislation that helped served as the prototype for the federal plan upheld last month by the Supreme Court.

Fewer than one in five voters, 16 percent, said they wanted to know more about Romney's religion. The GOP presidential candidate is seeking to become the first Mormon to win the White House.

President Obama's campaign has been attacking Romney's decision to limit his tax disclosure to just two years — the 2010 filing he released earlier this year and 2011 returns he says will be forthcoming when they are ready.

Some Republicans have echoed the Democratic calls for Mitt Romney to release more of his returns.

In the Pew poll, 36 percent of voters said they wanted more information about Romney's tax returns. This included 35 percent of independents surveyed, along with 56 percent of Democrats and 18 percent of Republicans.

Obama and his campaign also have criticized Romney over Boston-based Bain, which he cofounded and led. The Democrats have spotlighted job layoffs and outsourcing by companies that dealt with Bain.

Romney, who cites his business background as the qualification that shows he can improve the economy as president, faced attacks on Bain during the race for the Republican presidential nomination.

The Pew survey shows that 35 percent of voters wanted to know more about Romney's record at Bain, including 37 percent of independents.

Among Democrats, 42 percent wanted more information on this subject, while among Republicans the figure was 27 percent.

There was no partisan divide concerning Romney's 2003-2007 gubernatorial term. The poll found 44 percent of Republicans, 41 percent of Democrats and 42 percent of independents wanting more information.

Overall, 69 percent of voters said they had enough information about Romney while 28 percent wanted more.

For Obama, 90 percent said they knew enough about him while 8 percent said they wanted to learn more.

The survey of 798 registered voters taken July 19-22 had a margin of error of plus or minus 4 percentage points for its entire sample.