http://www.italiangen.org/igg005.stmInformation on Italian citizenship for U.S. citizens of Italian descent
If you were born in the United States you may also be considered an Italian citizen if any one of the situations listed below pertains to you:
1) Your father was an Italian citizen at the time of your birth and you never renounced your right to Italian citizenship;
2) Your mother was an Italian citizen at the time of your birth, you were born after January 1, 1948 (and before April 27, 1965) and you never renounced your Italian citizenship;
3) Your paternal grandfather was an Italian citizen at the time of your father's birth and neither you nor your father ever renounced your Italian citizenship;
4) Your mother was born in the United States, your maternal grandfather was an Italian citizen at the time of her birth, you were born after January 1, 1948 and neither you nor your mother ever renounced your rights to Italian citizenship.
and more . . .
I looked into this for jollies about 2-3 years ago. Unfortunately, we could not find any of my grandfather's papers.