Police on Thursday arrested a man who allegedly shot dead a woman outside her house in Madhya Pradesh's Dhar city after she rejected his marriage proposal, an official said. There was an exchange of fire between police and the accused, who also suffered bullet injuries, before he was nabbed, he said. The accused, Deepak Rathore, on Tuesday shot the woman dead outside her house in Basant Vihar Colony when she was starting her scooter and preparing to leave for the court in connection with an old case involving his mother, police said.