A CBI source said that the agency made the decision after considering a possible delay in the 21-month-old unsolved case by the departure of the officer, who was handling the case.
Kaul was part of the Special Investigation Team (SIT), constituted in Sep 2009 to probe the case.
The investigation into the Aarushi murder case has been hit by many hurdles.
SIT had to be reconsituted in Sep 2009 after two of its key officer Joint Director (JD) Arun Kumar and Superintendent of Police (SP) Vijay Kumar was transferred.
Kumar, an Indian Police Service (IPS) officer, was repatriated to the Uttar Pradesh cadre, while the SP was shifted to the agency's anti-corruption wing.
Under the supervision of Kumar, SIT had arrested suspects- medical assistant Krishna Thadarai, domestic helps Rajkumar Sharma and Vijay Mandal and had reached its conclusion based on narco analysis test through which Thadarai and Sharma confessed to the crime, while Mandal was apparently a witness.
The reconstituted SIT, while treating the trio as suspects, are verifying possible leads.
Recently, Aarushi's parents, dentists Rajesh and Nupur Talwar were made to undergo narco analysis test.
14-years old Aarushi Talwar was found murdered in her room on May 16 2008.
While the police were suspecting Hemraj Banjade, the domestic help as the accused, his body was later found on the terrace of the house.
In an apparent attempt to cover up their lapses, Aarushi's father Rajesh Talwar was arrested by police on charges of the double murder. But he was later released due to lack of evidence against him.