Check the year of manufacture on the right side of the chamber area. If 1938 or later (pretty sure of the year) it'll be stamped 6.5 or 7.35 on the flat just ahead of the rear sight's fixed blade. Earlier manufacture - 1891 through 1938 - were exclusively 6.5x52mm. Some Carcanos were converted to fire the 7.92x57mm Mauser cartridge - I'd imagine for last ditch use by the Volkssturm in '45, but I've no idea where or in what manner the caliber change was marked, if at all.
With a 1944 date it almost certainly would've been part of the RSI's inventory up north, and with that in mind I'm pretty sure it's a 6.5mm. For the RSI to have manufactured, maintained stocks of, and fielded both types of Carcano cartridges (6.5x52mm and 7.35x51mm) would've been a logistical nightmare for a government whose days were already numbered.