The accident occurred at Gangarampur under Bishnupur police station when the three bus passengers, including a woman, were sitting by the window with their elbows sticking out.
While two of the severed hands fell on the road, the third one went inside the driver's cabin of the truck laden with fish, police said.
The truck driver threw the hand back inside the private bus plying in route number SD-26 and fled with the vehicle.
Both the bus and truck were going towards Kolkata and were racing each other, police said.
The bus was seized but the driver fled while the truck driver ran away with the vehicle.
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