Police registered a case under Section 23 of Juvenile Justice Act against them, as per which they can be punished with imprisonment for six months or a fine or both.
Kannur Superintendent of Police P N Unniraja told PTI that the statements of the parents and the organisers would be taken today.
The incident evoked sharp reactions state-wide with Kerala Human Rights Commission registering a suo motu case against them.
He said the child's mother has 60 hours of flying experience and wanted to rear her toddler for the same without giving a thought to the fact that she was too small.
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"What is alarming is that there are no norms and guidelines fixed for such adventure sports," he said.
K E Gangadharan, Member of the Commission, said efforts should be made to ensure such incidents do not recur.
The organisers -- Malabar Adventure Sports Society -- claim they train cadets of NCC and Nehru Yuvak Kendra and come under the umbrella of the National Adventure Foundation.
Kerala State Commission for Protection of Child Rights said the incident was violative of the Child Rights Convention and action could be taken against the parents under JJ Act.
On May 3, Kannur Collector P Balakiran was injured when his paraglider developed a snag at a height of 25 feet and he fell down.