You've never met my chief! He has asked how many handguns, how many rifles, how many shotguns. I don't know if he asks for a list too, as I shut him down when he did that and another friend (former COP in another town) did as well. He just backed off when I told him MGL doesn't require it and I'm not giving that info to anyone. But this is a "routine" question for him. Both of us held LTCs for close to 20 years prior to that line of questioning.
Yes, they can ask anything they want, you aren't obligated to answer non-required questions. How you handle it depends on whether you are willing to stand up for your rights or fold when asked to piss in a cup, give a DNA sample, provide a list of all guns with S/Ns, etc. Most chiefs/LOs aren't this nosy, but some are.