Calvi was found hanging from a bridge and his death has never been fully explained. He was chairman of Banco Ambrosiano, in which the Vatican bank held a small stake.
Besides the 500-or-so inhabitants of the world's smallest state, the Vatican bank serves thousands of Catholic charities, religious orders and dioceses around the world. It has some 33,400 accounts and about $8 billion in assets.
Experts believe the risk of financial crime at the Vatican to be low. But they're concerned that the bank's global reach, high volume of cash transactions and lack of information about some account holders could make it a target for organized crime.
The Moneyval report led to the suspension of card payments at Vatican shops and museums for six weeks earlier this year after the Bank of Italy refused to give Deutsche Bank approval to continue operating systems within the city-state.
Payments resumed last month after the Vatican struck a deal with Switzerland's Aduno to provide the service, sidestepping the regulatory authority of the Bank of Italy, which is restricted to EU-based financial institutions.