Leaving with Cat from Turin to U.S. with Alitalia

I cannot find forms, stickers, or anything else to get form the carrier for my cat (he will go on cargo). I cannot get a straight answer from Alitalia and no idea what a passport means, as I came to Italy with my cat and went to small town first where the vet did not fill out forms.
What can I do? Help, leaving in June and have a very healthy cat. I have the last vaccination record. Can I download a form for airline from somewhere?