A Greater Manchester Police spokesman said:
At approximately 10.45pm last night two GMP officers had stopped another car.
When they got out to speak to the occupants it was driven into them.
The vehicle then left the scene.
One of the officers has some broken bones and the other has a fractured skull.
They are in a stable condition in hospital.
More top news
The 38-year-old man is said to be in a serious condition after the fall and the girl is said to be stable.
The man who called by as Stefano Brizzi was allegedly strangling PC Gordon Semple said he thought someone was "throwing up on the carpet".
Michael Danaher, 50, killed book dealer Adrian Greenwood at his home over a £50,000 first edition copy of Wind In The Willows.