He was produced before a city court on Tuesday and Metropolitan Magistrate, 3rd Court, Calcutta, Jyotirmoy Bhattacharyya granted three-day transit sought by the Enforcement Directorate (ED) to take him to Mumbai, where the case was registered.
Kulkarni is allegedly linked to the overseas businesses of Choksi, one of the main accused in the case, and the ED had notified a look out circular against him, the officials said.
A Mumbai court had also issued a non-bailable warrant against him.
Choksi, his nephew and diamond jeweller Nirav Modi and others are being probed under various criminal laws after the fraud came to light this year, following a complaint from PNB that they allegedly cheated the nationalised bank to the tune of about Rs 14,000 crore in connivance with some PNB employees.
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