Cospito has been on a hunger strike since October to protest against the tough 41 bis prison regime that he is being held under and is usually reserved for mafia bosses.
His supporters have embarked on a wave of threats, acts of vandalism and violent protests,including rioting last weekend in Turin.
The CSM procedure seeks to defend the judges, including the supreme Court of Cassation judges who rejected his appeal against being held under the 41 bis, saying they had been subjected to "denigration" and "widespread, indiscriminate delegitimisation".
When the supreme court rejected Cospito's appeal, protestors told the judges they were "killers" who had "sold out" by handing down a "death sentence" based on a "political decision".
ANSA