BJP leader Mukul Roy was among the four people to be booked on Sunday in connection with the murder of Trinamool Congress MLA Satyajit Biswas in West Bengal's Nadia district, a senior police officer said.
Roy, on his part, said the decision to name him in the FIR was "politically motivated".
Mukul Roy, the accused is a former TMC member of Parliament, joined the BJP last year after his relations soured with Chief Minister Mamata Banerjee.
According to media reports, two of the four people named in the FIR have been arrested.
When asked to the police officials about the chances of the assailants fleeing the area, the officer said the state police has been put on a high alert.
"Nadia shares border with Bangladesh and there could be a possibility of them (assailants) trying to escape to the neighbouring country. Police have been put on high alert to check the movements along the border," official said.
"As per our primary findings, it seems that the victim was fired from behind and the act was the result of a well-planned plot. A country-made revolver used to shoot the MLA has also been recovered." the officer added.
Satyajit Biswas (41), who represented Krishnaganj constituency in the state assembly, was shot from point blank range by unidentified assailants on Saturday evening inside a Saraswati puja marquee at Phoolbari area in the district bordering Bangladesh.
He was immediately taken to a local hospital where doctors declared him "brought dead".
Claiming that the attack was a conspiracy by the BJP, TMC secretary general Partha Chatterjee said Saturday that those involved in the killing will be punished after a full-fledged inquiry.