The US insurance market isn't terribly "standardized" (actually, it's not terribly well regulated, either, but that's another topic for another discussion) and I've found in practice that even the insurers over on this side of the pond may ask for different documents. In Germany, my insurer wanted my state "driving record" - and when I requested that from the state of California, what I got back was a blank sheet of paper, that was supposed to indicate I had no tickets, no infractions and no other "issues" - but the Germans were a little freaked out by it.
Some prefectures here seem to ask for your "driving record", while others don't. Probably not a bad idea, in any event, to get some sort of statement from your insurer that indicates any and all discounts you receive - whether for "no claims" or whatever. Another thing that "counts" in playing the insurance game is longevity with your last insurer (and of course the statement from the insurer that you've been a customer for "X years" or whatever).
Cheers,
Bev