You do not need census records, unless you are using them to prove something that you cannot easily prove with the standard set of vital records which you would submit in an application.
You need to get an apostille on every non-Italian vital record (birth/marriage/death) that you include in the application. Then, you have to permanently release the paper to the Italian government.
For that reason, you will probably want to keep the old certificate as an heirloom and get a new birth certificate for your grandfather. Then, you would send the certificate to a higher level of government for an apostille.
In the United States, apostilles are given by the Secretary of State (or Commonwealth) of the state where the vital records originate. An apostille functions as an authentication of a record, and the signature of the government employee who produced it.