Tough call...but not really a realistic one
During the North Hollywood bank robbery, with the bad guys wearing (homemade?) body armor, and the cops 9mms not being able to bring them down, they went to a local gun store and "borrowed" some AR-15s. Gun shop owners apparently had no trouble with this, even though it technically violated CA law (unless there was an exception for LEOs which I don't know about).
I think it would be a tough call, because the only realistic reason the cops might need your guns is that there are some really bad dudes out there who need to be stopped NOW. And if that is the case, what civic minded citizen could rightly say no?
I find it hard to imagine a situation where there is both a need and the cops not having what they need for arms, AND knowing that you do. Many depts today have AR-15s, and unless you are a big Full Auto collector and have a barn full of belt feds, what are you going to have that the police already don't have access to? And if the police need belt feds to manage the situation, better call out the militia and the regular military.
Now, there may be a time when, while they do have heavier weapons, they don't have them with them, and borrowing from you (assuming you have any), might be faster, and faster in a situation that critical can mean lives. So, I think the obvious situation would be to say to the cops, "Fine, deputize me, and I'll start loading up!" This doesn't mean I expect you or me to do a dynamic entry or anything like that, but by being deputized, you have a duty (and a right) to be on the scene, and you should function in an advisory role. Because, if you have something the cops don't, that means that they haven't trained with it, and likely don't know how to best use it, and you do. So, not only do you get to keep an eye on your hardware, you are in the position of actually trying to help. This makes you a "good guy" and will likely do some good when things settle down, and you try to get your stuff back. If they view you as "one of us", there is a significantly reduced probability of your weapons being "lost", held as evidence, or some other BS delays in them being returned.
Actually I find this a rather unlikely scenario, as the cops will much more likely go to a gun shop, or even a dept store to get "emergency supplies" before they come to your house. And in any local where such stores are not to be found (like inner city areas), it is even less likely that there will be a civilian, with legally owned weapons of the kind and type the police would need. And even if there were, the odds of the officers on the scene having that information seem pretty small, at least to me.
There maybe a crack house at the end of the block just chock full of illegal ARs and AKs, Uzis and Macs, but I don't see the cops asking to borrow them, first because they wouldn't know (for sure) they were there, and second, the residents of said crack house likely would not take such a request well. They might even resist, and if they have the kind of firepower the cops already need and do not have, well, now the cops have 2 major problems instead of just one. Only thing I can see coming out of that kind of situation is political pundits in and out of uniform calling for more gun control, while standing over the caskets of officers who were "just trying to make the streets safe".