A 17-year-old was found in the same area with arm injuries.
Police have now asked for anyone who knows how the men were injured to come forward to help their investigation.
A West Yorkshire Police spokesman said: “Police were called to Sovereign Court, Bradford at 7.56pm yesterday after a 43-year-old man was found with a head injury.
“Enquiries in the area found a second male, aged 17, who was also taken to hospital for treatment to an arm injury.
“Enquiries are continuing today to establish how these males came to be injured and anyone who may be able to assist is asked to contact Bradford District CID on 101, quoting log 1581 of 11 January.
“Information can also be reported anonymously to the independent charity Crimestoppers on 0800 555111.”