The Catalog of Copyright Entries has:

(BOOM, BOOM) AIN'T IT GREAT TO BE CRAZY
Words, Josephine Moore Proffitt; music, Sidney Lippman
© Sidney Lippman, 24 Oct 1952, EU291897.

Billboard magazine from Feb 21, 1953 lists a record release:

AIN'T IT GREAT TO BE CRAZY
b/w IF THE END OF THE WORLD CAME TONIGHT
Recorded by Ginny Gibson, Jubilee 6027.

Strangely, there is another listing in the Catalog of Copyright Entries:

BOOM, BOOM (AIN'T IT GREAT TO BE CRAZY?)
Words and music by Nick Noble & Dick Gleason
© Studio Music Co., 10 May 1962, EP163232.

There was an earlier listing in 1942, but I am unable to see the whole thing.

My guess is that it was already circulating in public domain when several people decided to copyright their own version of it.