A man was found with head injuries and no memory of what happened to him in Connaught Road on Sunday.
A Good Samritan found the man, who is believed to be Polish, at about 12.30am and contacted the emergency services.
He believes the victim, 34, had flagged down a silver Vauxhall Insignia for help but these people, two men, left prior to the ambulance arriving.
Det Con Helen Toms said: “I would urge anyone who heard or saw anything suspicious between 11.30pm on Saturday night (Feb 22) and 12.30am on Sunday morning (Feb 23) to contact the police to help piece together exactly what happened to this man. I am particularly interested in tracing the two men in the Insignia as they were speaking with the injured man and they may be able to recall their conversation and may have vital information as to how the man was injured.”
Anyone with information relating to this incident can contact DC Toms at Luton Police Station, in confidence, on 01582 394091, or Bedfordshire Police on 101, or text information to 07786 200011.