The main opposition RJD, however, rejected the charges levelled by the senior BJP leader, saying he was suffering from "lalu phobia".
Modi alleged that Prasad and his family used the Awami Cooperative Bank, headed by former RJD MLC Anwar Ahmed, for converting black money into white, taking loans from it and exchanging scrapped Rs 500 and Rs 1000 notes post note ban.
"The CBI and the Enforcement Directorate should probe the role of Prasad and the bank in the matter," he said.
Ahmed, the bank's chairman, is considered close to Prasad and was a nominated member of the state Legislative Council.
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Modi claimed Prasad's account number S/B A/C 1001 and Rabri Devi's S/B A/C 6651 were still active. He said Prasad's account had a deposit of Rs 58 lakh, while that of Rabri had Rs 15.62 lakh.
The deputy chief minister, who also holds the finance portfolio, said the state government would also get the matter probed by its agencies.
He claimed central agencies found evidence of transaction of Rs 10-12 crore through 70 benami accounts with the bank during a raid at the office of a trust headed by Ahmed.
The RJD dismissed the allegations as baseless and without substance.
"Sushil Modi is suffering from Lalu phobia. He has lost mental balance...Have you ever heard of banks indulging in any such illegal activity of converting black money into white. This is sheer his imagination. The charges are baseless and without substance," RJD spokesman and MLA Shakti Singh Yadav said.
The family has been under the Income Tax department and Enforcement Directorate's lens in connection with benami land deals and tax evasion. Some properties belonging to Prasad's MP daughter Misa Bharti and his son and former deputy chief minister Tejashwi Yadav have also been attached.
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