In a letter to her, Mr Katju sought action against policemen who arrested Jadavpur University professor Ambikesh Mahapatra and farmer Shiladitya Chowdhury, the first for circulating a cartoon of the Chief Minister and the second for questioning her policies.
The former Supreme Court judge also said that former Joint Commissioner of Police Damayanti Sen be restored to her earlier office, from which she was removed after she cracked a rape case on Park Street.
"We all make mistakes but a gentleman is one who realises his mistake and apologises. I request you to act against the policemen who ordered and implemented the arrest of Mahapatra and Chowdhury, you should immediately withdraw the cases against them and apologise to them."
Mr Katju said Ms Banerjee's ministers and bureaucrats "are afraid to speak out their minds fearlessly before you, and are terrorised by your unpredictable and whimsical behaviour".
Stating that her ways were "very unhealthy", he said Ms Banerjee "will not be able to remain Chief Minister for long unless she changed her ways and became more tolerant. It is still not too late if you listen to my advice and change your ways. I had praised you at one time. But of late you seem to have become increasingly intolerant and whimsical."