The pistol was given to the girl by her mother, thinking it was a toy, police added.
According to police, Kakoli Jana found the pistol in a garden outside their house at Khanakul in Arambag on Sunday morning and mistook it for a toy.
As the girl was playing with it, she fired it accidentally, shooting her mother in the back, a police officer said.
"The injured woman was rushed to Arambag Hospital. Her condition is critical," he said.
"The girl said the pistol suddenly went off and the bullet hit her mother sitting in the room. She is in a state of shock," the officer said.
Police said they are investigating how the pistol came to be in the garden.
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