Strauss-Kahn, a one-time French presidential hopeful whose chances were derailed by a sexual assault accusation in New York, arrived at the police station in the northern city of Lille for a prearranged morning appointment. He hadn't emerged by Tuesday night and French media reported that he would be held overnight.
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Police are probing a suspected prostitution ring in France and neighboring Belgium that has implicated police and other officials. They have questioned prostitutes who said they had sex with Strauss-Kahn during 2010 and 2011 at a luxury hotel in Paris, a restaurant in the French capital and also in Washington, D.C.
French law permits police to question Strauss-Kahn for up to 96 hours with a judge's approval.
Strauss-Kahn lived in the U.S. capital while he was head of the IMF before resigning his position in May after he was charged by New York police with making a hotel maid perform oral sex. The charges were later dropped.
Two men with ties to Strauss-Kahn have been put under preliminary investigation in France on charges including organizing a prostitution ring and misuse of corporate funds.
Strauss-Kahn's name surfaced in the investigation last fall and his lawyer has asked that his client be allowed to tell his side of the story. One of Strauss-Kahn's lawyers has said that the former French presidential hopeful never knew that the women at orgies he attended were prostitutes.
"He could easily not have known, because as you can imagine, at these kinds of parties you're not always dressed, and I challenge you to distinguish a naked prostitute from any other naked woman," Henri Leclerc told French radio Europe 1 in December.
Strauss-Kahn, 62, has been married for two decades to journalist Anne Sinclair, recently named editor of the upcoming French version of the Huffington Post.
French newspapers have dubbed the investigation "The Carlton Affair" after the name of the expensive Lille hotel where some of the meetings took place.
Investigators are seeking to discover if prostitutes were paid using corporate funds from a large French construction company, Eiffage.
"If these parties and these trips across the Atlantic were being financed by a major French group for purposes of prostitution obviously that puts a lot of people in deep trouble because it is a misuse of corporate money," said Christopher Mesnooh, a legal expert who is not linked to the Strauss-Kahn case.
The case is unconnected to the attempted rape accusations in New York.
New York prosecutors dropped the case against Strauss-Kahn in August because the accuser had undercut her credibility by lying about her background and changing her account of her actions right after the alleged attack. She says she was truthful about the encounter and is pursuing her claims in a lawsuit.
Strauss-Kahn has said the sexual encounter was "inappropriate" but not violent.
In a separate case last October, French prosecutors refused to pursue an allegation by a young French writer of attempted rape by Strauss-Kahn.
The Paris prosecutor's office said Strauss-Kahn admitted during questioning to actions amounting to sexual assault but couldn't send the case to trial because it happened too long ago. Writer Tristane Banon said Strauss-Kahn tried to rape her during a 2003 interview for a book she was writing, when she was 23.