According to the police, three assailants pumped bullets into Kumar, general secretary of BJP's Patna unit, near his residence near Daldali Road in the city.
The incident sparked protests in the area. BJP MLAs created a ruckus in Bihar Legislative Assembly and Legislative Council over the killing, alleging the incident reflected the "deteriorating" law and order situation in the state.
Top BJP leaders met the victim's family and held a meeting at state party headquarters and issued a 48-hour ultimatum to the police to arrest the culprits else they would launch an agitation.
Police have got closed-circuit television footage from a temple, which showed the attackers chasing and shooting Kumar.
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"The footage shows three assailants chasing Kumar on foot. They shot him and he fell on the road. One of the assailants then walked up to him and shot him in the head. All the attackers escaped after committing the crime," a police officer said.
The SSP said a Special Investigation Team (SIT) has been formed under Deputy Superintendent of Police (DSP) Ramakant with 25 other officers for probing the murder case. He also said two persons have been taken into custody in this regard and were being interrogated.
"We are probing the case from all angles including Kumar's enmity with neighbours over ward council elections. I am personally monitoring the case and we will make efforts to ensure arrest of all involved both in the actual incident, as well as, the larger conspiracy," Vaibhav added.