Does a hospital know if you dual apply in their system?

I'm thinking of dual applying psych and FM, but there's a specific (large) city that I want to stay in. If I apply to both psych and FM at the same teaching hospital will they know that I dual applied to 2 residencies in their system? I would do that for all of the programs in my city if I'm not likely to get caught.
Source: Student Doctor Network - Category: Universities & Medical Training Authors: Tags: Medical Students (MD) Source Type: forums