South Yorkshire Police said the car crashed in Stainforth after failing to stop for officers and running out of control on a bend last night.
The driver of the car fled the scene.
In a Facebook post, the Doncaster East Neighbourhood Policing Team, said: “This vehicle was dangerously driving round the estate, it ended with the driver failing to negotiate a bend and crashing in to a house. The driver made off on foot.
“If you have any information that could could assist with identifying the occupants of the vehicle please get in touch.”
Officers in the police team are also keen to trace the riders of two black motorcycles who were reported to have been ‘flying round the area’.
The team said: “These are a risk to the whole community, they are riding on paths and weaving in out of traffic on the roads with no regard for anyone's safety.
“If you have any information that would assist with the identity of the males on these bikes please get in touch. “Someone is going to get hurt.
“We want to work with you as a community to help make the area a safer place.
“All information is treated in the strictest of confidence.
“This isn't about being a grass, it's about helping to look after your community, and keeping people safe.”
Call South Yorkshire Police on 101 or Crimestoppers, anonymously, on 0800 555111.