"Lamb to the Slaughter" - You're the Detective

If I was a detective  investigating the murder of Patrick Maloney in “Lamb to the Slaughter” by Roald Dahl, I would have going to people that have last seen the person that was murder plus go see his family and his friends so I could know where he was last seen or where was he going to or any information if he was at his friends house for a  party or something. I would be an police detective.