The 31-year-old Astori was found dead in his hotel room in Udine hours before his team was to face Udinese and a day before signing a new contract with the club.
"An inquiry has been opened for culpable homicide against persons unknown," said head prosecutor Antonio De Nicolo. "It is a duty to ascertain if the death of Astori came about through tragic a fatality or if someone could have foreseen something."
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Earlier, Italian Olympic Committee president and acting head of Serie A Giovanni Malago called to refrain from speculating over the cause of Astori's death.