A disturbing video went viral on Twitter on May 3. In the video shared by @rajivtulli69, a man can be seen talking to some people not visible in the video, and a woman lying on the floor, presumably unconscious.

The man can be heard saying in Bengali, "Where were you when she backstabbed me?". When someone asks whether that gave him the right to kill, the man said "Why not?"
At the end of the video, the man can be seen violently stabbing the woman a few times. The video was shared with the caption “Love Jihad case at Baharampur, Murshidabad. Hindu girl refuse [sic] to accept His religion of peace so he stabbed [sic] her in public. Welcome to Islamic State Of Bengal. The victim is a student of Murshidabad Bahrampur Krishnanath College. Sutapa Chowdhury, a third-year student.”

Fact Check

In a reverse image search of the keyframes of the video, a video report from Behrampur on May 2 by ABP Ananda was found.

The report also states that the woman was from Malda, and the police are suspecting that a romantic relationship may have developed between the accused and the victim. The woman was first shot, then stabbed, according to the report. Witness Subhadip Paul can be seen in the video, alleging the accused had a gun in his hand, preventing the onlookers from rushing in to rescue the woman. No communal angle was mentioned in the report. 
On further investigation, an Ei Samay report was found on the incident.

The report stated that the woman, 21-year-old Sutapa Chowdhury was a third-year student at Krishnanath College of Behrampur. She was killed by Sushant Chowdhury, a resident of Malda and alleged lover of Sutapa. During a police interrogation, the youth said that he killed the woman because she had been unfaithful.
SP of Murshidabad, K Sabari Raj Kumar, gave his statement on the issue to the media in a video.

In conclusion, the viral video is falsely being given the angle of 'love jihad'. Neither the media nor the police gave any statement that could introduce a communal angle to the incident.