Dominique Strauss-Kahn, the financial power broker whose political career was ruined last year after he was accused of attempted rape in New York, was held overnight on Tuesday for a second day of questioning by police officials in the northern French city of Lille in an investigation into a prostitution ring accused of operating in France and Belgium. On Tuesday, Mr. Strauss-Kahn presented himself voluntarrily to the Lille investigators who wanted to question him about accusations of complicity in activities related to prostitution in Paris and Washington, where two businessmen are accused of paying for orgies in 2010 and 2011. A lawyer for Mr. Strauss-Kahn appeared to confirm that he had attended the events, saying that his client would not have been aware if the women who entertained him were prostitutes.