His lawyers said they would instead seek bail from the CJM's court, Alipore.
On February 11, the Alipore District and Sessions judge had rejected Mitra's bail prayer, after which he had moved the high court.
Two judges of the high court have already recused themselves from hearing his bail prayer citing personal reasons.
Mitra is in judicial remand since his arrest by CBI on December 12 for alleged complicity in the multi-crore rupee Saradha chit-fund scam.