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It happened at around 6am on Friday in College Lane in Worlingham in Suffolk.
The woman was not seriously hurt but sustained injuries to her arms and legs that were treated by ambulance personnel at the scene. Her dogs were not hurt.
Police need to speak to the driver of the car and are asking the person involved, or anyone who knows who he or she is, to call PC 1727 Bemment on 01986 835300.
Officers would also like to hear from anyone who saw the collision.