Which office holds the record
In Italy a death is logged by the registrar of the Comune where it happened. A doctor confirms it, the town hall writes the entry, and from then on the registry can print a signed copy for whoever asks. That signed copy is your working paper. Nothing you print at home carries the seal a foreign office is looking for.
Knowing how to apostille a Death Certificate matters most in the first weeks after a death, when banks and lawyers all write at once. Ask the clerk which version answers your case, because a short certificate and a fuller extract are not the same paper. Say which country will read it. The clerk will often tell you which one that country tends to send back.
The counter that adds the stamp
A registry copy is an administrative paper, so the Prefettura, the state office for the province, is the desk that stamps it. Rulings from a court and deeds signed before a notary are judicial or notarial, and those go to the Procura della Repubblica instead. Families dealing with a will may end up at both counters in the same week.
The province is fixed by the registrar who signed. To apostille a Death Certificate in Genoa the entry has to sit with a Comune inside that province, whatever the passport of the person who died. Where the death was logged elsewhere in the country, the office for that province owns the stamp and the file has to go there.
Fee and timing
The apostille cost for a Death Certificate in Genoa is a €16 tax stamp per document, and some documents are exempt. Records going to another country in the European Union can fall under an exemption, so ask the counter which case yours is. How long it takes depends on the queue and on how that office prefers to take files, in person or by post.
Estates, pensions and claims
The stamped record closes accounts, releases a life policy, transfers a flat, settles a pension and opens probate. A surviving spouse may also need it before marrying again abroad. Italy has been in the Hague Apostille Convention since 1978, so its member states take that single stamp without sending you to a consulate.
Language, and names that do not match
Add a translation where the reading office works in another language, and ask whether it must be sworn in front of a Tribunale, an Italian court, so the wording counts as accurate. The rules to apostille a Death Certificate in Italy are the same across provinces, while each bank abroad sets its own house style for the bundle it accepts.
Compare the spelling on the record with the passport and the will before anything is sent. Older entries sometimes carry a name in its Italian form, or a birthplace written as it was then, and an heir abroad can be refused over that alone. The legalisation of a Death Certificate in Genoa for a country outside the Hague list adds consular steps, so ask that country's desk early.