The court also rejected Kumar's prayer for quashing of a CBI notice that sought his appearance for questioning in the case.
Kumar sought seven days time, citing personal reasons, to appear before CBI officers in connection with the case.
A bench headed by Chief Justice Ranjan Gogoi and Justices Deepak Gupta and Sanjiv Khanna left it open to the Central Bureau of Investigation to act in accordance with the law.
Rajeev Kumar had been embroiled in a controversy for being at loggerheads with the CBI over its investigations into the Saradha chit fund and Rose Valley scams.
The bench said the affidavit has to be filed within two weeks and posted the matter for further hearing on March 26.
A two-judge bench comprising Chief Justice Ranjan Gogoi and Justice Sanjiv Khanna did not allow the application filed by some investors that despite the apex court's 2013 order directing the CBI to probe the chit fund scam, the investigation has not attained finality.
The officers, including DGP Virendra Kumar, were present at Banerjee's dharna venue on February 4 in plain clothes.
Irani said the Supreme Court had ensured that a free and fair investigation takes place.
CBI said Chief Minister Mamta Banerjee along with the DGP, additional commissioner of police sat on dharna or sit-in at around 10 pm Sunday in Kolkata and as such a conduct by the officials in uniform points to 'complete anarchy prevailing in Kolkata and West Bengal'.
The top court will hear the probe agency's applications on Tuesday. The CBI alleged that it has moved the application as an extraordinary situation has arisen in which the top police officials of the West Bengal Police are sitting on a dharna along with a political party in Kolkata.
Despite Prime Minister Narendra Modi assurance that issues raised by opposition parties will be discussed in Parliament, it does not seem sailing for the government in Parliament.
Ghosh in a suicide note has claimed that he consumed 51 sleeping pills. He has been admitted to the SSKM hospital in the city. However, it is yet to be ascertained as to how the ex-TMC member procured such a high quantity of sleeping pills in the jail.
Former Assam Director General of Police (DGP) Shankar Baruah, whose house was raided in connection with the multi-crore Saradha chit fund scam, has committed suicide.
CNBC-TV18‘s Ronojoy Banerjee, quoting sources, reports that the government has set up an inter-ministerial group to coordinate regulation of the financial sector.
Financial services secretary Rajiv Takru says, in an interview to CNBC-TV18, that a high-powered group has been set up to examine chit funds: Takru
Amid allegations of involvement of many politicians in Saradha chit fund scam in West Bengal, ruling Trinamool Congress today said all guilty would be punished by the state government.