Activists of both sides were beaten up while incidents of ransacking houses and damage to vehicles were reported across districts.
Trinamool activists alleged a woman at Sildanga area in North 24 Parganas' Ashoknagar was physically abused allegedly by one of her relatives and a local BJP leader for "not agreeing to support the saffron party" and her child sustained an injury while she was heckled.
"A complaint has been lodged in the case. According to it, a child got injured while her mother was physically abused. Later, the child was declared brought dead by the local hospital. One accused has been arrested," police said.
In Murshidabad, Trinamool workers alleged that S. Roy, a party leader and husband of a member of party-run Naoda gram panchayat was shot by some assailants on Monday.
"Investigation is going on and the person who sustained the bullet was advised to be shifted to Kolkata from the district hospital," police said.
A Trinamool worker's wife at Cooch Behar's Tufanganj was allegedly beaten up by the BJP supporters for refusing to contribute a token fund for the saffron party's celebration rally.
BJP workers accused Trinamool activists at North 24 Parganas of opening fire at North 24 Parganas' Nimta area due "political grudge" though the ruling party denied all the allegations.
In a conflict over capturing a party office, a clash broke out between workers of the BJP and the Trinamool at Ilambazar's Chhotochawk village in Birbhum district and bombs were hurled overnight at the village.
In another violent incident at Mayureswar in the same district, a Trinamool supporter was beaten up allegedly by the saffron party workers in a clash.
Alleging that false cases were slapped on their party workers, the BJP held a protest demonstration at the Mayureswar police station after security personnel arrested two of their supporters for allegedly being involved in the incident.
BJP's Birbhum leader Kalosona Mondal on Monday courted controversy as he threatened the district police officials, saying that party workers would pull out policemen's tongues if they continue to harass their activists.
( With inputs from IANS )