Closer published the pictures, which were taken during a private holiday in France, in September.
Officials said they are investigating Ernesto Mauri, the head of publishing company Mondadori, and Valerie Suau, a photographer, for invasion of privacy.
Suau has denied she took any topless pictures, the BBC said, and magazine representatives have argued that photos were taken from a public road and were not offensive.
The duke and duchess of Cambridge launched legal proceedings after the photos were published, and a Paris court then banned Closer from republishing the images and ordered the magazine to hand over the original photographs within 24 hours.
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