I have a Winforms application (checkers game) which have a local DB (using SQL Server Express) to save the registered players and their scores..
I\'m trying to crea
Provided that the conditions to use local DB at the client machine are OK (see LocalDB deployment on client PC), in the deployment project you can just add the database files to the application folder (Choose File System Editor in the solution explorer when the deployment project is selected.

Side note: Are you aware of the fact that in VS2012 the MSI deployment project template is deprecated?
Addition: And it's back in VS 2013!