The official web site of the state of Montana confirms that Montana has a "state ballad" as well as a "state song"—but it says the state ballad is MONTANA MELODY, adopted in 1983. Click here for lyrics.

I was able to find a couple of references to John Nelson "Sleepy" Hall, but he's pretty obscure, at least as far as his full name is concerned.

There was a band leader of the early jazz era called Sleepy Hall, who performed as Sleepy Hall and His Collegians, but I'm not convinced he's the same person. Some sources say "Sleepy Hall" was a pseudonym of Gene Kardos or of Chick Bullock. Maybe there was more than one Sleepy Hall?

ASCAP.com lists GREEN HILLS OF MONTANA written by Francis Hall and John Hall, with Colgems EMI Music Inc as the publisher.

Oddly, neither WorldCat nor the Library of Congress lists such a song.