Police later found that three youths, who are suspected to have been be in an inebriated condition, were in the car when the mishap occurred last night.
Ms Kokila S Kumar, a councillor of Kollam Corporation, died on the spot while her father Mr Sunil Kumar, 50, succumbed at a private hospital in neighbouring Thiruvananthapuram in the wee hours today.
The accident occurred when they were returning home after attending an Onam celebration organised by a local residents association.
The car was cruising at a high speed when it hit the two-wheeler from the rear and halted briefly before speeding away, police said.
Local people who reached the spot immediately, said the occupants of the car were allegedly in an inebriated state.
Police have identified the owner of the car, which was found abandoned at a house at near Sakathikulagara.
Police said a search is on for the three youths.