Strictly speaking, an air safety investigation wouldn't be compulsory, since the relevant regulation (REGULATION (EU) No 996/2010) mentions an obligation to investigate only in case of accidents and serious accidents. In the definition of these categories, it is specified that an accident/serious incident is an occurence that
takes place between the time any person boards the aircraft with the intention of flight until such time as all such persons have disembarked.
An empty aircraft would not be included.
However the same REGULATION (EU) No 996/2010 states that...
Safety investigation authorities may decide to investigate incidents other than [accidents and serious incidents] in accordance with the national legislation of the Member States, when they expect to draw safety lessons from them.
So far, no information has appeared on the Italian ANSV website. Usually they publish a short notice when a new investigation is launched.