Officers want to speak to anyone who was in the area and saw a grey VW Tiguan.
A 17-year-old women was taken to hospital where she remains in a critical condition.
The car believed to have collided with her, a grey Volkswagen Tiguan, left the scene.
It was later recovered from an address in Roston Drive, Hinckley, and two people were arrested.
A 33-year-old woman was arrested on suspicion of causing serious injury by dangerous driving and drive a vehicle whilst unfit through drugs and was released under investigation.
A 39-year-old man was arrested on suspicion of causing serious injury by dangerous driving, failing to co-operate with a preliminary test and criminal damage and remains in police custody.
Sergeant Stu Parker from the force’s Roads Policing Unit, said: “This collision has left a young woman with some serious injuries and we are keen to speak to anyone who was in the area at the time of the collision.
“The car travelled down Factory Road, on to Tudor Road and then onto Hollycroft.
“Anyone who was in the area and saw a grey VW Tiguan and can give us any information that may assist the investigation, we want to speak to you.
“If you have any dashcam footage, please submit it to us.”
Visit Making a road traffic incident report | Leicestershire Police or call 101, quoting crime number 24*692642.