It is not totally clear what you want to do here. You also do not state which version of GTK+ you are using.
All this does is create a new window, the window will be on the default screen and will need to be populated with the widgets you want to make it of any use. You can create as many windows as is needed for you application.
Not sure if I am thinking of the same thing you are? You can set your window to another screen. This could be a different monitor or the same monitor but a different screen. The function to call is
void gtk_window_set_screen (GtkWindow *window,
You did not say which version of GTK+ you are using as the method of obtaining the GdkScreen is different between the versions. Most applications do not need to have windows on different screens. The applications that I do know of that take advantage of multiple monitors are video presentation, and audio/video editors where having multiple monitors is very useful.