The music - I have my doubts

Having originally seen this film on the big screen as a child I've grown to love it over the years.
I have my doubts about the music credits though. David Rose and Henry Mancini are both credited as the composers, yet listening to the music it sounds very much like composer Paul Smith's work.
Smith was doing a lot of work at the time for Disney and later Universal, etc.
He scored the final seasons of leave it to Beaver (also Universal), and this film, being shot at Universal would be a perfect vehicle for his talents.
My gut feeling is that Paul Smith is the primary composer for Operation Petticoat.