An Apostille is a separate document which is issued under the Hague Convention and is accepted by all countries that accept the terms of this convention. Italy, the USA, Canada, Great Britain and Australia are among many others who belong to that group.
An apostille is a document which verifies that the certificate issued is a true copy of the original (i.e Brith, Marriage, Death Certificate). Normally translations of apostilles are not required, but some Italian Consulates still insist.
Apostilles will be required for documents written in English if they are for use in (for example) Italian Citizenship applications. This is to assure the Italian Consulate and Comune that the documents are not false. It should follow - and normally does - that an apostille is therefore not required for an Italian document if it is issued for that reason.
But being aware of the vagaries of some consulates, your best bet is to check the website for the consulate where you are or ask them yourself. It is difficult to give you further guidance as you have not shown where you are... in the USA, Canada, Great Britain, Australasia etc. etc. Or the reason for needing the certificate you mention.
If you are seeking Italian Citizenship then this web site may be useful: >Apostilles and Dual Citizenship<