Lagarde, the former finance minister of France, interceded in the case between Bernard Tapie and the bank Credit Lyonnaise, which was then state owned, Radio France Internationale reported Wednesday.
Lagarde cut the court case short by sending it to private arbitration, which ended up awarding Tapie $578 million in taxpayer money.
Tapie had contended the bank owed him money after it handled the sale of the Adidas sportswear brand. It is thought that he did not end up with the entire $578 million in his own bank account, Radio France Internationale said.
But Tapie was a friend of French President Nicolas Sarkozy, who was Lagarde's boss when she was the French finance minister.
The Court of Justice of the Republic has requested three appeals court magistrates investigate her role in the affair, specifically to look into charges of "complicity in forgery" and "complicity in misuse of public funds."
Lagarde was named head of the IMF in June as a replacement for Dominique Strauss-Kahn who resigned to concentrate on a legal defense of his own. He is accused of attempted rape of a hotel maid in New York.