The incident took place last week.
A teenager arrested on suspicion of murder has been released on bail.
Officers were called to reports of an assault at around 10.40pm on Thursday, 23 January near to Alfreton Park off Wingfield Road in Alfreton.
On arrival a 49-year-man was in a critical condition, East Midlands Ambulance service attended and he was taken to hospital where he died on Friday, 24 January.
An 18-year-old man who was arrested on suspicion of murder last week has been released on police bail with conditions whilst enquiries continue.