Please try this connection string
SqlConnection conn = new SqlConnection
{
ConnectionString = "Data Source=" + System.IO.Path.GetDirectoryName(System.Reflection.Assembly.GetExecutingAssembly().GetName().CodeBase) + "\\Database.sdf"
};
alternatively you are use Relative path as below
ConnectionString = "Data Source=|DataDirectory|\Database.sdf";
Modifying DataDirectory as executable's path:
string executable = System.Reflection.Assembly.GetExecutingAssembly().Location;
string path = (System.IO.Path.GetDirectoryName(executable));
AppDomain.CurrentDomain.SetData("DataDirectory", path);