Is suppose, this has nothing to do with asp.net. Since desktop applications are Windows Forms or WPF (not true for Win8).
As I understood, you don't need an actual server since the only client of it would be the application. That is what embedded servers are for. There are many of them, so you have to choose, but for the simplicity's sake, I suggest trying
Microsoft SQL Server Compact edition[
^]. And here is a good tutorial how to use it:
http://www.c-sharpcorner.com/UploadFile/3cf852/an-introduction-to-sql-server-compact-edition-sqlce-4-0/[
^]. Since it needs no separate installation during the deploy process, you can ship all your files and the database using the normal deployment (setup) process you would use for the gui part of your application.