I don't have the game, so this is just from what i picked up here and there :)
Try to send a Scout to the district , then click on the City Hall to 'dig deeper'.
If it doens't work the first time around, try it again at some different time of day.
Edit: here's a more detailed explanation i found at the neoseeker forums on a post made by shagura:
"Make sure your knowledge is very high in that particular area, you may need to investigate the area several times to do this. Once you have say 90 to 100% knowledge send your guy out to investigate it again. Set a reminder for this action so it automatically takes you to him when he starts investigating. Now all you do is click on the house you need to dig deeper and it will come up with a different sign than other houses. If you click on it your man will investigate that house extra while out on 'patrol'."
Link to the thread in question over at neoseeker.