The state CID is likely to send a team to Aligarh to try and arrest Mr Varshney, who had on camera declared a "bounty of Rs 11 lakh" for Ms Banerjee.
The announcement of the bounty by the BJP Yuva Morcha leader on a video created nationwide furore, with politicians cutting across party lines demanding stringent action against Mr Varshney. The BJP also distanced itself from the controversy by disowning its leader.
Calling Ms Banerjee a "demon", the BJP youth wing leader had said, "When I saw the video, I only had one thought... that if anyone gets me Mamata Banerjee's head I will give them 11 lakh."
The youth wing leader had said that he was deeply hurt at a lathicharge on Tuesday on a crowd at Birbhum, about 180 kilometres from Kolkata, when they had had gathered to celebrate Hanuman Jayanti.
He told reporters that he made this announcement in a fit of rage and emotional outburst after seeing video footage of the lathicharge in West Bengal.
A police case has also been filed against Mr Varshney by Aligarh district Trinamool Congress President Ramphool Upadhyaya at the Civil Lines Police Station in Lucknow.
With inputs from agencies
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