I read somewhere that they straddled it. The Iowa sank the Katori in same egagement. Sank her after the fifth salvo.

A brief account of the entire battle can be found here http://www.combinedfleet.com/katori_t.htm starting with the dates 17-18 February 1944.

That account says that Iowa "closed with Katori", so the range was probably quite a bit less. On the other hand here is a discussion from a few years back that claims that Iowa did not hit Katori, at least with her main battery. That poster states that Iowa only hit a destroyer and an auxiliary ship with her secondary 5" guns. I'm still looking for a more detailed account.
http://warships1discussionboards.yuku.com/topic/5270

[edit] A little further down the poster Tiornu states that Iowa's own after-action report claims they did hit Katori, and with the main battery. I used to correspond semi-regularly with Tiornu (real name Richard Worth) and own one of his books. I trust his judgement an qualifications, so it's probably true. Either way it's an interesting discussion.

I have read several places that it was the Iowa that sank her. The Katori had many huge holes in her, not typical of a 20 kg 5" shell. The place that I read about the battle said she fired High Capacity shells (HE). Those shells weight almost 900 kg. Maybe this might add to the confusion, since those shells would make smaller holes than the 1200 kg super heavy AP shells.