The police constables were struck at garages behind homes in Westacre Crescent, Finchfield, in the early hours of Saturday morning.
They were responding to reports of a burglary when they came across the car. When they approached the car sped off, hitting them both.
One of the PCs, a woman, suffered serious leg injuries. She was released from hospital yesterday. A male officer was taken to hospital with minor injuries.
The Peugeot 407 was later recovered by police around one mile away in Windmill Crescent near Smestow School.
Pictures of the recovered car, which is a distinctive blue colour, have now been released and West Midlands Police are appealing for information.
Detective Inspector Greg Evans, said: "We have got a vehicle which has been recovered which has been subject to an extensive examination. We are suggesting that it may be linked to the matter.
"If anybody has knowledge of someone who has previously driven that vehicle, or who has been in that vehicle, or has any knowledge of who owns it, then let us know."
The hit-and-run happened at the garage site in the quiet residential road, near its junction with Limehurst Avenue.
At the weekend, the Chief Constable of West Midlands Police, Dave Thompson, branded it a "dreadful crime."
Speaking to the Express & Star yesterday, Det Insp Evans, added: "I wholeheartedly agree with Mr Thompson. The officers were merely responding to a call from a member of the public who needed their help.
"As a result of them doing their public duty they have been subject to a serious assault with a vehicle which could have resulted in much more significant injury and indeed loss of life.
"I would appeal for anyone who knows who was responsible for this crime to assist the police enquiries and I even appeal to the person themselves, to their better nature.
"We don't find this sort of offence very often thankfully, but when public servants are targeted this way it brings home the value of the work they do to keep the streets safe."
Det Insp Evans explained that further enquiries were needed to identify a suspect given that registration plates on cars involved in burglaries are frequently and illegally changed.
Anyone with information can call 101 giving reference 79 04/11, or Crimestoppers anonymously on 0800 555 111.