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The CBI has been given a month to examine the footage and devices like pen drives and determine if there is enough material to merit a First Information Report, which outlines the basic charges and evidence against the players.
The "Narada sting tapes" were released to news channels before last year's state election in West Bengal, which saw Ms Banerjee being re-elected with a huge lead.
The sting showed people resembling 11 Trinamool ministers and leaders accepting cash from Narada journalists who posed as the representative of a fictitious company seeking favours from the government.
The Trinamool described the footage as doctored and a smear campaign.
The High Court last week said that a forensic lab had reported that the footage appeared genuine.
Mathew Samuel, editor of Narada News, told the court that the recordings were done using an iPhone.
The High Court had said that the state police's role in the investigation amounted to that of "puppets on a string" controlled by the government. Judges also criticized the government for acting with "all the vehemence at its command."
Challenging the CBI inquiry, Ms Banerjee's government said it was unfortunate that what the High Court had ordered was exactly what state BJP President Dilip Ghosh had said after the UP election results were declared. Its lawyer had to apologize today for alleging bias by the High Court.
The Trinamool Congress has recently been singed by the arrests of two senior leaders for alleged involvement in a Ponzi Scheme called the Rose Valley Chit Fund in which small-time investors were gypped of savings through an unregulated fund.
Trinamool leaders like Madan Mitra and Sandhir Agarwal have also been accused of close links to the Saradha Group, a conglomerate that went bust in 2013, wiping out as much as $3.7 billion in deposits from mostly low-income families. Saradha had some Trinmaool MPs on its payroll.
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