Joni used a dulcimer for 'A Case of You', I'm certain. I've seen the clip, and others of Joni doing ACOY, numerous times over a few years, and always took the 'guitar-thingy' to be a dulcimer. It's not like any true guitar I've ever seen.

Maybe Joni would care to enlighten us - you there Joni?? (Now wouldn't it cause a stir if the Great Lady actually responded? But I'm not holding my breath!) :-) :-)