The 20-year-old student, Nina De Chiffre, was snapped by a photographer working for AFP as she went to kiss the policeman, Salvatore Piccione, at a protest against a new high-speed rail line in the Alps.
Her act was interpreted by many as a loving gesture and proved a hit on social media, although the photographer Marco Bertorello and De Chiffre herself pointed out that it was intended as an act of mockery.
Franco Maccari, the head of the COISP police union, earlier this month vowed to sue the protester for "sexual violence and insulting a public official".
Contacted by AFP, prosecutors said they had not received a lawsuit but said one could still be submitted for 90 days after the protest.