The party supporter, 32-year-old Amal Halder, was standing in a queue before a polling booth at Joynagar when a CISF man opened fire, the party said.
It alleged that a police officer of Joynagar police station escorted a CISF contingent while polling was in progress at Mayahauri village.
It said that it was not known on whose order the firing by the CISF man took place as there was no law and order problem at the booth.