WASHINGTON — Federal documents filed by Mitt Romney’s former company appear to conflict with the Republican presidential candidate’s statements about when he left Bain Capital, the private-equity firm central to his legacy in the private sector.

In a filing with the Securities and Exchange Commission in February 2001, Bain Capital listed Romney as the company’s “sole shareholder, sole director, chief executive officer and president.” It said Romney’s “principal occupation” was as Bain’s managing director.

Romney’s campaign repeatedly has said Romney had virtually nothing to do with the company’s operations after February 1999, when he began work on the troubled 2002 Winter Olympic Games.

Romney “left Bain Capital in February of 1999 to run the Olympics, and had no input on investments or management of companies after that point,” campaign spokeswoman Andrea Saul said Thursday.

Questions about Romney’s control at Bain from 1999 to 2001 are important in his bid to oust President Barack Obama this fall. That’s when the company oversaw investments that either sent jobs abroad or filed for bankruptcy. It’s also a time during which Romney stated in federal disclosure forms that he was not active in Bain Capital.

For example, in late 1999, Bain-controlled Steam International set up overseas call centers, and a subsidiary moved jobs from California to Mexico. In 2000, the Ampad company declared bankruptcy. The following year, so did steel-maker GS Industries — just as Bain made $58.4 million from its investment.

The two presidential campaigns differ about the extent to which U.S. jobs were affected. But the Romney camp’s chief response long has been that Romney wasn’t making decisions for the company when these events took place.

The campaigns exchanged sharp accusations Thursday about truthfulness and the issue of sending U.S. jobs to other countries.

Stephanie Cutter, Obama’s deputy campaign manager, said Romney may have committed a felony if he misrepresented his role at Bain on the SEC documents. And if he was running Bain after 1999, Cutter said, Romney hasn’t been truthful with the public.

“If that’s the case, if he was lying to the American people, then that’s a real character and trust issue,” she said.

Romney’s campaign, meanwhile, released a new TV ad titled “No Evidence.” It accuses Obama of falsely depicting the former Massachusetts governor as someone who shipped jobs overseas when he ran Bain Capital. The ad, which will run in several battleground states, asks voters: “When a president doesn’t tell the truth, how can we trust him to lead?”

The SEC document from February 2001 — which has received modest attention despite being reported in recent days by publications including Talking Points Memo — raises questions about Romney’s role at Bain in 1999, 2000 and early 2001. If he turned his full attention to the Olympics in early 1999, as his campaign says, it’s hard to square with the Bain SEC filing, two years later, listing his “principal occupation” as the company’s managing director, and his titles as CEO and president.

Romney’s campaign issued a statement Thursday from Bain that said Romney “left Bain Capital in February 1999 to run the Olympics and has had absolutely no involvement with the management or investment activities of the firm or with any of its portfolio companies since the day of his departure. Due to the sudden nature of Mr. Romney’s departure, he remained the sole stockholder for a time while formal ownership was being documented and transferred to the group of partners who took over management of the firm in 1999. Accordingly, Mr. Romney was reported in various capacities on SEC filings during this period.”