Vivek Tiwari was shot dead on Saturday by a police constable in Lucknow.
Delhi BJP leader Ashwini Upadhyay Monday lodged a police complaint against Chief Minister Arvind Kejriwal over the latter's tweets in connection with the shooting down of a tech company executive in Lucknow.
Mr Upadhyay, who is also a Supreme Court lawyer, sought registration of a case against Mr Kejriwal accusing him of "promoting enmity on grounds of religion" and "doing acts prejudicial to maintenance of harmony". He filed the complaint against the chief minister at Tilak Marg police station.
Police said the complaint was being looked into.
"We are seeking legal opinion on whether a case can be made out with regard to the complaint," a senior police officer said.
The Aam Aadmi Party (AAP) supremo had on Sunday hit out at the Bharatiya Janata Party (BJP) over the killing of Vivek Tiwari, claiming "the BJP does not protect the interests of Hindus".
Mr Tiwari (38) was shot dead on Saturday by a police constable in Gomti Nagar area of Lucknow when he did not stop the car for checking.
In a series of tweets, in Hindi and English, Mr Kejriwal had slammed the saffron party over the incident.
"Vivek Tiwari was a Hindu, right? Then why was he killed? BJP leaders rape Hindu girls across the country? See it clear. BJP is not well-wisher of Hindus. If they have to murder Hindus for power, they won't think twice," he said in a tweet in Hindi.