Post Office Smoking

I am confident it is Rota's. It sounds quite close to the score he done for Visconti's Boccaccio '70 segment, The Job.

maybe it is an old italian folk song.

see:
Good morning sun - Piero Umiliani but also
Vocal theme - Donimak (Nico Fidenco) -Tamborelli - Morfina

here from an interview w/ umiliani:Have you ever used pseudonyms as a composer? 
Yes, lots of times. I produced too much, and at RAI we couldn't have too many tunes done by the same author. So they let me put the weirdest names on the tunes, Zalla, Moggi, and others that I can't remember.

Yeah, I had this confirmed elsewhere. It is Umiliani. Rota gets some attribution on the IMDB page, which seems to be in error. Oddly, it's not the only film which wrongly credits Rota also (Mafia as well).