The TMC leader is at present in judicial custody following his arrest on August 11 by CBI in connection with the cattle smuggling case.
The accused, Sudipta Roy, was nabbed from BNR More in Asansol city on Monday night for allegedly threatening special CBI judge Rajesh Chakraborty with a drug case.
Judge Rajesh Chakraborty wrote to Paschim Bardhaman district judge on Monday requesting him to take note of the "threat" and bring it to the notice of the Registrar of the Calcutta HC.
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The CBI on Wednesday visited Mondal's Nichupatti residence in Bolpur to question his daughter but left within 10 minutes after Sukanya refused to talk to them.
Sources said Mondal used Birbhum as the corridor to smuggle cattle to Bangladesh, and around 20,000 cattle were illegally sold during 2014-17.
CBI arrested Anubrata Mondal in a dramatic raid involving 100-odd CRPF personnel from his Birbhum residence after he skipped 10 summons citing ill health.
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Senior leader and minister Chandrima Bhattacharya said the TMC will not take any action against Mondal, the party's Birbhum district president, now and will wait for the law to take its own course.
Mondal rose to prominence in the 11 years of the TMC regime in Bengal, mostly for his audacious statements and browbeating.
The smugglers used to ferry animals from Ilambazar to Indo-Bangla border under the alleged protection of Mondal and local Trinamool leadership from state enforcement agencies, they said.
MP Santanu Sen added that the party has "zero tolerance" on corruption and wrongdoings. The top TMC leadership will likely meet in the evening to take a call on the issue.
Mondal, who is in his 60s, is scheduled to appear before CBI sleuths again on Wednesday in connection with the probe, after having skipped Monday's session.
Cattle smuggling case: CBI finds 'involvement' of Anubrata's bodyguard as Trinamool leader skips questioning
In the 40-page charge sheet, the CBI alleged that Hossain played a vital role in moving money from cattle smugglers to Mondal, who is the TMC's Birbhum president.
The TMC leader is on his way to state-run SSKM Hospital in the metropolis for a health check-up, a party source said.
Anubrata Mondal was interrogated by the CBI in connection with its investigation into a cattle smuggling case in West Bengal.
CBI's notice came after the Calcutta High Court on Tuesday upheld a single bench order which refused to grant Mondal protection from arrest in the case.