Cicci broke omerta and yes, his testimony that Michael was the boss of a crime family injured Michael's credibility as a respectable businessman. We're not shown what happened to Cicci because of the dramatic focus on Frankie. My guess is that Michael figured Cicci deserved to die, and that would be consistent with his policy of never giving an enemy a pass. But when Frankie recanted, Michael's problems with the Senate committee were solved. He induced Frankie to commit suicide because Frankie was the highest-level rat, and because, over time, Frankie might still have been an asset to the FBI in their pursuit of Michael. But Cicci, rat that he was, was no longer a threat to Michael. There was no Witness Protection Program at that time, so Michael could have arranged for Cicci to be murdered in prison by another inmate. But that might have stirred up speculation relating to Cicci's testimony against Michael, and he probably figured it'd be prudent to let the matter rest.