This is all speculation, rather than knowledge-based.
Could it be a conversion of a Fiat 600T van? There's a picture of one on Wikipedia and the lines are generally similar, particularly the radiator vent above the rear wheel but the rear side window is different which suggests a coachbuilt conversion. Given the rear engine, I don't know what the floor level of the 600T was, but judging by the hinge position for the lower tailgate it appears to be quite low.
The number plate says "Prova Roma 272". I'm no expert on Italian number plates, but I believe that a "Prova" plate is a temporary "trade" plate. In which case "Roma 272" would be registered to a particular company, which would be a big clue - it might even belong to the carrozzeria that did the conversion.
The "Conti" badge features a coat of arms so it could belong to a town, county (or Italian equivalent), owner, or maybe even a company.
Can any of our Italian members provide further information?