For the second time this year, legal officials chose on Thursday not to prosecute Dominique Strauss-Kahn on charges of attempted rape, despite what investigators here said was evidence of sexual assault, ending months of scandal that have tarnished a political career that once seemed destined to lead to the French presidency. There was evidence from Mr. Strauss-Kahn’s own testimony of sexual assault in a 2003 encounter with a French writer and novelist, Tristane Banon, the prosecutor said in a statement, but given a three-year statute of limitations on that charge, no case would be brought. “Facts that could be qualified...