One of the images, labelled as lasagne, showed a stack of rubble with bloody feet emerging from it.
Italian magistrates will decide whether the case can proceed.
The town of Amatrice, which was one of the hardest hit by 24 August`s 6.2 magnitude earthquake, is famous as the home of the dish called spaghetti all`amatriciana.
Charlie Hebdo`s controversial cartoon, titled "earthquake Italian style", showed a bloody man described as penne tomato sauce, an injured woman as penne gratinee, and bodies stacked between layers of rubble as lasagne.
The French publication`s office was the target of a terrorist attack in January 2015, in which 11 people were killed, prompting an international wave of solidarity with the magazine.
`Senseless and incomprehensible`
However, the Amatrice cartoon prompted widespread outrage on social media and in the Italian press, with many decrying it as insensitive.
In response, Charlie Hebdo released a second cartoon, with the caption "Italians ... it`s not Charlie Hebdo who built your homes, it`s the Mafia!"
Prosecutors in Italy are investigating whether earthquake safety regulations were followed in affected buildings.
They are also investigating possible corruption in the awarding of construction contracts or building inspection certificates, the Associated Press reports.
Mario Cicchetti, a lawyer for Amatrice, said the cartoons were "macabre, senseless and incomprehensible" and showed "contempt for victims of a natural disaster".
If the complaint goes to trial, and the French magazine is convicted, it could be forced to pay damages in a related civil suit.
"Any damages awarded to the town will be entirely turned over to the quake victims," Mr Cicchetti said.
Charlie Hebdo said it would not comment at this time.
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