FWIW, I did a quick search of ("March Madness" + "basketball") on Newspapers.com and found a slightly earlier reference. FYI, the nice thing about doing a search on Newspapers.com is it will show you a chart of the number of hits over a period of time.
In this case there was a slight uptake around 1982 (when CBS first gained rights to the NCAA tournmanet and as you mentioned Brent Musberger apparently started saying it) and then around 1986 it really started taking off. By around 1998 it had established current levels of usage.
Looking earlier, there was a slight uptick in the late 40's and the term was used spordically in the 1950's.
Going back to the beginning, I did see an article which talks about the use of "March Madness" but not in relation to basketball. It's from a 2-MAR-1925 article in the
Roanoke (VA) Times entitled
"March Blusters In Like a Lion" Below is an excerpt:
March, aside from the distinction it claims as the namesake of the Mars, regarded as the mightiest of the Roman gods, is unique in other respects. Formerly it was regarded as the first month of the year. It is also associated with madness for some unknown reason but the term "March madness" at one time was much in use and the superstition prevails that madness is most apt to take effect on a likely subject during that month. March has been employed to describe many things including a popular kind of beer, familiarly known as bock beer.
The first instance I could find of use of the term in relation to basketball was from 11-MAR-1931 in the
Rushville (IN) Republican which used the term
"March Madness" as a headline for a short article discussing high school basketball in Indiana noting the elimination of Anderson, Tech, Columbus and Shelbyville in regional tournaments.
The next hit was an AP story, also about Indiana High School basketball, and published in multiple Indiana papers on 5-JAN-1937 (
Richmond Item ,
Lafayette Journal and Courier and
Evansville Courier and Press), talking about the Indiana High School tournament the following spring where it notes:
INDIANAPOLIS, Jan. 4 - (AP) - Holiday tournaments over Indiana's high school basketball teams this week settle into the home-stretch before the annual "March madness" - the State Tournament.
......
So these uses predate the 1939 usage.