I believe that this is where you are in the walkthrough:
Backstage - Go to the alley and ring the bell. If no one answers, go to the front lobby door and knock on that door and then comeback to the backstage door. Then once again, knock and then ring bell. Give the calling card to the manager. He lets you in to talk to Abi.
Go to the stage and see Abi rehearsing. Talk to her about everything. Silk is the name of the illustrator.
As you can see, the walkthrough doesn't say anything about how you get to the police station from Red Chapel. And unfortunately, I don't remember what the deal is. It seems like you ought to be able to use the map, but I am of course not sure about that either.