Where should I put the LocalDB file?

Say I have a Visual Studio solution with three projects:

Application Layer - MVC
Data Layer
Domain Layer
Service Layer

The data layer uses Entity Framework. Say I want to add a localdb (mainly for testing). Do I add the 'SQL Database file' solution item to the Application Layer (MVC) or data layer. It seems cleaner to add it to the data layer so that multiple clients can access it.

If it is added to the data layer then how do I ensure that the file is copied to the BIN folder of the application layer each time it is built so that the application layer can see it? Ideally the database would not be refreshed every time the application layer is built.