By far the worst atrocities committed by Italy were during the invasion of Abessinya (Ethiopia) when the Italian army used mustard gas (!) against native African soldiers.
In WW2 Italy didn't commit atrocities, but I have heard it said that some Italian troops were ill disciplined and treated prisoners of war badly, even cruelly.
There were several incidents of attrocities that were committed on the Italian population by the German occupation forces. Most of these attrocities were retaliation for partisan attacks on their troops. In order to carry out these attrocities, they did get some help from Italians who were either soldiers or polititians, ones who were extreme Fascists. Here are some examples.
Pietro Caruso - Police Chief (Questore) of Rome. Executed on September 21, 1944 for assisting the Germans with massacre at Ardeatine Cave.
Nicola Bellomo was an Italian General. After the war, he was tried for war crimes for shooting escaped British POWs earlier in 1942 and was executed on 11 September 1945. Oddly, in 1943 he was an anti-Fascist and lead his army against the Germans and helped the Allies capture the port of Bari.