The issue relates to alleged non-disclosure of overseas assets and bank accounts held by Chidambaram's wife, son Karti and daughter-in-law Srinidhi.
Directing Chidambaram to cooperate with the investigation, a division bench headed by Justice Joymalya Bagchi kept her application for anticipatory bail pending.
CBI had recently filed chargesheet against her in a special court in Kolkata in connection with the Saradha Chit Fund.
CBI said that Nalini had received Rs 1.4 crore from Saradha group of companies, embroiled in a chit fund scam.
The dalit girl has scored top marks in the State Board Class 12 examination, but could not match it in the national test which is based on CBSE syllabus.