If CBV is open and in focus in some tab you can copy active bible reference to eg. OpenOffice by clicking Alt+P. But if another window is active and CBV is beyond in that tab, Alt+P will not work. It just render a beep sound.
Same is true if CBV is opened in an floating window.
One workaround is to open CBV in a very small window:

But I think it would be great if Alt+P (and Alt+C) could work regardless if CBV is open or not. As far as I use my current settings I then can copy and paste single verses or verse selections without having CBV in focus. I think that would be an improvement.