The video shows Banerjee speaking in the Lok Sabha in 2005 against infiltration in West Bengal as leader of the Trinamool Congress and claiming that many Bangladeshi voters figured in the state list. She is then shown throwing a sheaf of papers at then Deputy Speaker Charanjit Singh Atwal.
The video, captioned "CAB in Bengal is need of the hour", also contains footage of Banerjee's recent speech where she is seen railing against the Citizenship Amendment Bill (which has now become an Act after it was passed by parliament). This part of the video is captioned "CAB leads to civil war in the country".
Dhankhar had on Tuesday night tweeted the video circulating on Facebook with the comment "analytical video that stirs rational approach".
"They are running a fake video against me," Banerjee alleged during a protest meeting against the CAA.
She explained that the CPI-M led Left Front then did not allow fair polls and "there were people whose names used to appear 50 times on the voters list".
Banerjee said she had campaigned with the slogan "no id card, no vote", and on July 21, 1993, 21 workers of the Congress - her then party - were killed in police firing during an agitation on the issue. "Then finally, we succeeded in our moment," she claimed.
"Don't lie. Don't release fake videos. Some people are lying. It feels bad when the Home Minister also does that," she said referring to Union Home Minister Amit Shah who has questioned her change of stance since that time.
"And some people in constitutional chairs are following them up, and tweeting. Very unfortunate," she said, urging Trinamool workers to "resist" such propaganda on the social media.
"90 per cent of fake social media content is funded by the BJP. Don't believe it. Don't let them incite," she added.
( With inputs from IANS )