If you develop an application that use Sql Server 2012 as storage for
your data then you need to install it in a way or another. There are
numerous versions of Sql Server, like Sql Server Express and LocalDB. In
every case you need the bits that supports your coding calls.
This magazine article summarizes relevant infos on the
various version of Sql Server
I suppose that the right product for you is Sql Server LocalDB. A version of Sql Server that could
be distributed easily with your application setup and doesn't require a
complex installation procedure.
However, if you don't foresee the need to escalate you application to a
full Client-Server model and you need only a local storage for a single
user, you could choose a single file database like Sql Server Compact Edition or SQLite or even MS Access.