Kumar was questioned for more than five hours, sources said.
The officials had questioned and took statements from Kumar on June 26.
Charges were levelled against Kumar towards the fag end of the previous LDF rule by the present Chief Minister Oommen Chandy, who was then heading the Congress-led UDF opposition.
Besides irregularities in his appointment in IHRD, an autonomous educational institution established by Kerala Government, charges against Kumar also include foreign trips he had undertaken while serving as Managing Director of Kerala State Cooperative Coir Marketing Federation Ltd.