How to provide a SQL Server database with a C# application
I suppose that you have a setup kit to ship your application.

I also suppose that you want to ship an empty database with your application, with at most a handful of rows for built-in values in some tables.

The correct way to handle this is to include your database setup in your setup kit, so that it creates the database and all required objects (tables, views, procedures, users, logins, ...). 

One possible way to do this is to include a .dacpac file in your setup kit and invoke sqlpackage to deploy it to a target sql server instance. The .dacpac file should be obtained by building a database project in visual studio (SSDT).

If you don't have a database project or you don't have a setup kit, you should probably rethink your deployment strategy completely.