The sergeant received minor injuries and received medical attention.
A police spokeswoman said he would not be returning to duty today because of his injuries.
Police say they are concerned at the level of disregard shown, not only for the safety of their staff, but for members of the public and the woman and child in the stolen car.
The vehicle is described as a home-painted matte-black Nissan Terrano registration BMM872.
Police are asking anyone with information on the whereabouts of the vehicle or its occupants to phone 111 immediately or report anonymously via Crimestoppers on 0800 555 111.