When I entered into Rome mid June of this year, the immigration officer took my US Passport, entered something into the computer and said "ah!! 6 months in Italy and 6 months in the US", I offered my Italian documents (PDS etc.). She advised that she did not need to see them, We made some small talk and I was on my way. When I entered in March, same thing, my US Passport details were enough to determine that I am an Italian resident.