The agency is discussing it's next move by holding talks with their lawyers, a source related to the probe said.
According to the source, the CBI had summoned Kumar to appear before it on Tuesday at 10 a.m. at its Salt Lake office in Kolkata.
"But he again failed to depose before the agency," the source added.
Kumar did not appear before the agency also on Monday afternoon after he was summoned for a second time.
The source said that the agency has forwarded two letters to the Director General of Police (DGP) asking to share the reason of leave and Kumar's whereabouts.
"The DGP office has conveyed the CBI's message to Kumar and also about its summons to appear before the agency," he said.
The CBI had summoned Kumar for questioning first on Saturday, a day after the Calcutta High Court withdrew interim protection from arrest given to the former Kolkata Police Commissioner in the Saradha chit fund scam case that saw thousands of people lose their hard earned money with some pushed to the extreme point to end their lives.
The court had given the interim protection on May 30 and then extended it multiple times.
However, Kumar sent an email to the agency seeking a month's time to appear before the agency as he was on leave.
He was again summoned on Monday.
The investigating agency had in May sent a notice to Kumar asking him to appear before it and later issued a lookout notice alerting all airports and immigration authorities against him leaving the country.
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 the officer's residence and later held a 45-hour sit-in at the city hub on the issue. But in February itself, as per the Supreme Court order, Kumar was interrogated by the CBI in Shillong.
( With inputs from IANS )