Bora, who was working in Mumbai, was allegedly killed by her mother Indrani Mukerjea, a former media executive, and two others.
The court extended co-accused Peter Mukerjea's interim bail in the matter till the final disposal of his regular bail plea.
The 65-year-old, who is in jail since his arrest by the CBI in 2015, was Sunday admitted to the state-run J J Hospital after he complained of chest pain.
Chidambaram's alleged role came under the scanner of investigating agencies in connection with the Foreign Investment Promotion Board (FIPB) clearance of Rs 305 crore.
INX Media Ltd, which was owned by Mukerjea, had allegedly paid bribes to get a Foreign Investment Promotion Board approval, which was facilitated by ex finance minister P Chidambaram's son.
The ED has summoned some ex-Finance Ministry officials, who were handling FIPB issues in 2007, in connection with its money laundering probe in the INX media deal case.
Karti Chidambaram was arrested by the CBI on Wednesday on the basis of confessional statements of INX Media Limited directors Peter and Indrani Mukerjea.
The CBI today justified Karti Chidambaram's arrest in the INX Media case in a Delhi court by taking the ground of his non-cooperation and frequent foreign visits.
Mukerjea had demanded access to the personal diary maintained by sub-inspector Ganesh Dalvi, a prosecution witness who was part of the team that arrested prime accused Indrani Mukerjea's driver.