The only way I know to do this is to traverse the tree of windows until you find what you’re looking for. Traversing isn’t hard (just see what xwininfo -root -tree does by looking at xwininfo.c if you need an example).
But how do you identify the window you are looking for? Some applications set a window property called _NET_WM_PID.
I believe that OpenOffice is one of the applications that sets that property (as do most Gnome apps), so you’re in luck.