The 13-year-old boy was treated for injuries to his back and elbow following the collision in Romanby, near Northallerton, on Sunday evening.
North Yorkshire Police said officers were now trying to trace a white Porsche in connection with the collision.
The injured boy was hit while on his bike on Yafforth Road in the Castle Hills area at around 7pm on Sunday, August 31. Paramedics were called to the scene and he was taken by ambulance to James Cook Hospital in Middlesborough where he was treated for a severely-grazed back and bruised elbow.
He has since been discharged.
Officers said they were also keen to speak to two cyclists who were on Yafforth Road, Romanby, heading towards Yafforth at the time of the incident, who may have seen something.
Anyone who witnessed the collision or saw the Porsche which was in the area at the time, or who has dash cam footage, is urged to contact North Yorkshire Police.
Support The Yorkshire Post and become a subscriber today.
Your subscription will help us to continue to bring quality news to the people of Yorkshire. In return, you'll see fewer ads on site, get free access to our app and receive exclusive members-only offers.
So, please - if you can - pay for our work. Just £5 per month is the starting point. If you think that which we are trying to achieve is worth more, you can pay us what you think we are worth. By doing so, you will be investing in something that is becoming increasingly rare. Independent journalism that cares less about right and left and more about right and wrong. Journalism you can trust.
James Mitchinson (Editor)