Kumar's lawyers filed the petition at the Alipore district and sessions court on Friday and served a notice on the CBI.
Moving the petition, Kumar's counsel said he was only the investigating officer of the scam, and that the CBI has never said he was involved in the scandal or any of the crimes associated with it.
The counsel said so there was no need for his custodial interrogation.
Opposing the bail plea, the CBI lawyers called Kumar - currently the Additional Director General of state Criminal Investigation Department - an absconder.
Despite being a protector of the law, the former Kolkata police commissioner has now turned into a law breaker, the CBI counsel argued.
"There are multiple points. We have raised each and every issue concerned with this offence and this case.
"We have seriously objected to the anticipatory bail application considering the social ramification and considering the importance of investigation, considering the fair and transparent investigation as directed by the honourable apex court," the CBI counsel told reporters after the hearing.
Objecting to the CBI calling Kumar an absconder, his lawyer submitted he had informed the federal agency on August 28 that he was available for questioning till September 1, but would not be available then till September 25. So in such circumstances, "how could he be called an absconder?".
After hearing both sides, the court turned down Kumar's application.
Two days back the CBI had moved a plea for issuing non-bailable arrest warrant against Kumar in Alipore court, but Additional Chief Judicial Magistrate Subrata Mukehrjee disposed of the prayer, saying the former Kolkata police commissioner could be arrested by the CBI in accordance with law if it feels that is needed as the higher courts have withdrawn the protection from arrest given to him earlier.
The judge also observed that the CBI could approach the court if it faced any adverse situation while making the arrest.
On Tuesday Kumar had moved an anticipatory bail plea in the district sessions court of Barasat, but the judge ruled the petition "not maintainable" saying the case had been generated in the South 24 Parganas district while his court has jurisdiction over North 24 Parganas district.
The Alipore court is the district court of South 24 Parganas.
The court had given the interim protection on May 30 and then extended it multiple times.
The investigating agency had in May sent notice to Kumar asking him to appear before it and later issued a lookout notice against him alerting all airports and immigration authorities against him leaving the country.
Kumar had moved the court on May 22 seeking quashing of the CBI notice asking him to appear before the agency.
He appeared before the CBI on June 7 and was grilled for several hours.
Kumar, who headed the Special Investigation Team (SIT) in 2013 that probed the Saradha scam, is accused of tampering with evidence in this case.
The Supreme Court in May, 2014, handed over the case to the CBI.
The CBI is seeking Kumar's custodial interrogation arguing certain documents seized by the SIT during the initial investigation into the scam were not handed over to it.
( With inputs from IANS )