Officers were called to a collision on the A32 at 3.30pm on Tuesday, May 3, involving a red Seat Ibiza and a silver Audi TT.
A 23-year-old man who was travelling in the back of the Audi suffered "life-changing injuries" and is currently being treated at Southampton General Hospital.
The 39-year-old female driver of the Seat and her 10-year-old daughter suffered whiplash injuries.
Acting police sergeant Melanie Adcock said: “We know that there were other vehicles in the area at the time of the collision so we would like to hear from those motorists. We would like to speak to anyone who witnessed the collision or who saw either vehicles prior to the incident.”
Anyone with information should APS Adcock on 101, quoting 44160166204, or Crimestoppers anonymously on 0800 555111.