Ms. Lagarde has repeatedly denied any wrongdoing and has expressed her willingness to cooperate with any investigation.

Gerry Rice, the director of the External Department of the monetary fund in Washington, declined to comment on the case on Wednesday, but he said the fund’s board had discussed the possibility of French legal proceedings against Ms. Lagarde before its decision to appoint her as managing director in 2011. The board at the time “expressed its confidence that Madame Lagarde would be able to effectively carry out her duties,” Mr. Rice said in a statement.

In a statement, Ms. Lagarde’s lawyer, Yves Repiquet, said she hoped that the results of the police search would enable the truth to be established and would “ultimately lead to the termination of all investigations.”