Kumar's lawyers filed the petition at the Alipur court. The hearing may take place on Saturday around noon.
CBI sources said they have received a notice about the anticipatory bail plea of Kumar, who is currently the Additional Director General, CID.
Meanwhile, the investigative agency sleuths raided a resort in Bishnupur area of South 24 Parganas district and went to a few buildings on south Kolkata's Camac Street and Lake Town in the city's north east fringes.
The CBI officers also visited 34, Park Street - Kumar's official residence - and asked his wife about his whereabouts. They left the building after over an hour.
On Thursday, CBI officers had searched for Kumar at an Indian Police Service (IPS) officers' mess at Alipur and a five star hotel near Ruby Hosptial crossing off the Eastern Metropolitan Bypass.
On Thursday, 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 off 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Commissioner could be arrested by the CBI in accordance with law if it feels that is needed as the higher courts have withdrawn the protection from arrest given to him earlier.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.
Three days back Kumar had moved an anticipatory bail plea in the district session court of Barasat but the judge ruled the petition as "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 Alipur 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 a 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 as the Commissioner of Bidhannagar police 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 was not handed over to it.
An unprecedented chain of events had unfolded on February 3 when a CBI team reached Kumar's residence to question him. The team was detained and taken to a police station before being released.
West Bengal Chief Minister Mamata Banerjee had also visited his residence and later held a 45-hour sit-in here on the issue. But in February itself, as per the Supreme Court orders, Kumar was interrogated by the CBI in Shillong.
( With inputs from IANS )