Imagine a floor to ceiling window with a big hole in it because someone has jump through it. If you saw that window would you describe it as broken or shattered or something else?
Two police officers ran into the office and saw the broken/shattered/* window.
"Broken" is a fairly general word - it could mean anything from the frame being jammed, through to the glass being entirely gone - and you should be aware that it refers to the window as a whole.
"Shattered" is far more specific - it means that there is extensive damage to the glass itself, though not necessarily a hole. (Think of a car windscreen, or other safety glass, which remains in one piece despite being covered in cracks.)
So, in this case, either term would be fairly equally appropriate - "broken" might be better for a formal context, while "shattered" better for something like a new article, where a little sensationalism is acceptable.
"Shattered" means that the glass has not just cracked, but actually broken into pieces.
So, if you mean the window glass now has a crack, or multiple cracks, but is still holding together; or perhaps that some of the glass has come out but the rest remains in the frame, say that the window is broken.
If you mean that the glass now lay on the ground in many pieces, say that the window is shattered.
