A woman is in hospital after she reversed her car into a backyard pool in Sydney's west with her six-year-old daughter inside.

Police said the 37-year-old woman was first spotted driving erratically in the lower Blue Mountains, west of Sydney, on Monday afternoon.

Officers said a car was involved in a police pursuit through suburbs including Penrith and St Marys, but they stopped the chase due to concerns for the welfare of the driver.

An unmarked police car then started following the woman after police received some information from the public.

Police again spotted the car heading east on the Great Western Highway about 6:20pm with a child in the passenger seat.

The vehicle continued, driving at the speed limit on the M4, allegedly driving erratically and turned off at Wallgrove Road.

At this point officers made another attempt to pull the car over but it failed.

Police said the car then turned into Tarragen Avenue, Hobartville, and officers followed it.

Officers said the driver then put the car into reverse and accelerated "harshly" causing the car to crash through a fence, landing in the pool.

The officers jumped into the pool and rescued the girl and her mother.

The woman was medically assessed at the scene and taken to Nepean Hospital and the child is with her father.