Officials said Nalini did not appear today and is understood to have suggested to the ED sleuths that she should rather be questioned at her residence, as allowed for women under CrPC provisions.
It was not immediately known as to what the ED would do now and whether it would issue fresh summons or take a legal opinion before initiating fresh action.
She was also asked to carry documents related to her personal finances and those related to her engagement with the Saradha group.
The matter pertains to the legal fee paid to Nalini, a Supreme Court lawyer, by the Saradha group, official sources said.
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The amount in question is Rs 1.26 crore, they said, noting the Enforcement Directorate (ED) wants to understand the exact flow of funds to her from Saradha company accounts and the contract made therein.
The sources said she has now been summoned in the "light of the new evidence".
Saradha chairman Sudipta Sen, at present in jail, had mentioned about hiring Nalini as a lawyer at the request of Manoranjana Sinh, estranged wife of Congress leader Matang Sinh.
Nalini represented Manoranjana and hence was asked to offer her professional advice in her negotiations with Sen in connection with plans by the group to acquire a TV channel in the northeast.
The agency, till now, has issued four orders for attaching properties worth about Rs 600 crore in this case.It registered a case under PMLA in 2013 taking cognisance of police FIRs of West Bengal, Assam and Odisha.
ED has pegged the amount of the scam at Rs 2,500 crore and has conducted an investigation involving lakhs of multi-layered transactions.