Eminently plausible that the song might still be in copyright in the USA.

Back in 1929, under the 1909 US act, copyright came in two terms - each of 28 years from the investing of statutory copyright (usually either registration or publication with a correct copyright notice). The second HAD to be acquired by renewal and if it wasn't renewed teh song went out of copyright in the USA (not necessarily elsewhere - lots of fun in other jurisdictions). So - then copyright might have lasted until 1985.

But by the 1976 US copyright Act, copyrights were extended. By the Sonny Bono extension Act they were extended again. Lots of useful shit on the LIbrary of Congress website. Yet more fun follows from the US Berne COnvention Implementation Act.