Emergency services were called to reports of the accident involving a pedestrian and a car on Main Road, Slyne, Lancaster just after 6pm on Tuesday, February 20.
The pedestrian, a lady in her 80s, was taken to hospital with injuries to her hip.
Police are now appealing for witnesses to come forward with any information which could help them with their investigation.
A police spokesman said: "We were called to reports of a collision involving a Toyota Yaris and a pedestrian.
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"The vehicle was travelling south on the A6. As it approached the brow of the hill, it made contact with the pedestrian, causing her to fall."
"The pedestrian was taken to Royal Lancaster Hospital where she remains in a serious but stable condition."
Anyone with information can contact police on 101 quoting log number 1160 of the February 20.