After a fourth round of questioning before magistrates on Wednesday, Lagarde said she was returning to her work in Washington, and called the investigation "without basis." She is the third IMF managing director in a decade to face legal troubles.
Lagarde and her former chief of staff have faced questions about their role in an arbitration ruling that handed 400 million euros ($531 million) to a French businessman with a checkered past.
"After three years of proceedings, dozens of hours of questioning, the court found from the evidence that I committed no offence, and the only allegation is that I was not sufficiently vigilant," she said in a statement.
Under French law, the official investigation is equivalent to preliminary charges, meaning there is reason to suspect an infraction. Investigating judges can later drop a case or issue formal charges and send it to trial.
Defence lawyer Yves Repiquet said the negligence claim was "paltry," ''extremely minor," and "unfounded," and said investigators could not make a valid case for tougher penalties. He said he will file a motion to have the preliminary charge dismissed.
"There was no reason for her to resign," Repiquet said by phone. Lagarde will not be required to answer questions for the case for months at the least, he said, insisting it will have no impact on her ability to do her job.
The charge could bring up to a year in prison and a fine of 15,000 euros.
"We're nowhere near that just yet," said lawyer Christopher Mesnooh of Field Fisher Waterhouse. "This will probably not go to any kind of a trial or a next stage until next year at the earliest."
"It's a very complicated matter, with enormous political and legal ramifications."
The 400-million-euro payment was awarded to Bernard Tapie, a flamboyant and high-profile businessman, in a dispute over the sale of his majority stake in sportswear company Adidas nearly a generation ago.
Tapie sought to sell his stake in the mid-1990s, asking bank Credit Lyonnais to handle the deal. He felt the sale was mishandled and sued the bank, which at the time was owned by the French state.
At the heart of Lagarde's questioning was her role in the unusual decision to handle the case by private arbitration, rather than through the French legal system.
Critics say the case should not have gone to arbitration because state funds were involved. Many also felt the deal was too generous, and was symptomatic of the cozy relationship between money and political power in France.
Lagarde became finance minister in 2007 under then-President Nicolas Sarkozy, the first woman to hold the post in a G-7 country. Tapie was a prominent supporter of Sarkozy. Before buying control of Adidas, Tapie had been embroiled in several scandals, including match-fixing in the early 1990s that led to an eight-month prison sentence.
The court investigating the payment has been set up specifically to deal with allegations of wrongdoing committed in public office. Lagarde's former chief of staff Stephane Richard — now head of the French telecom giant Orange — and Tapie both are under formal investigation for fraud.
Lagarde's predecessor at the IMF, Dominique Strauss-Kahn, quit after he was charged with attempted rape in the United States. The New York charges were later dropped. Strauss-Kahn is charged with aggravated pimping in a separate case in France.
A previous IMF chief, Rodrigo Rato, faced allegations of fraud in Spain after the bank he led as chairman collapsed. The collapse of Bankia came well after Rato's tenure in the Washington-based IMF ended in 2007.
Louise Dewast amd Jamey Keaten in Paris contributed to this report.
Follow Lori Hinnant at: https://twitter.com/lhinnant