A man was found dead with serious head injuries in a South Normanton churchyard at the weekend.
James Wood, 30, who lived in the area, was discovered by a member of the public outside St Michael's Church at around 5.45am on Sunday.
Two teenagers, aged 19 and from the South Normanton area, have been arrested on suspicion of murder.
Police sa
y they are keen to trace a man and a woman walking along Church Street at about 2am on Sunday, and a taxi driver parked on the corner of Church Street and Ford Bridge Lane at about the same time.
Detectives believe they may have seen or heard something that could help in the investigation.
Chief Insp Sandra Barker said: "We are appealing for any witnesses or anyone with information to contact police.
"We appreciate the support of the local community and are grateful to those people who have already come forward with information."
The death has sent shockwaves through the local community.
A nearby shopkeeper said: "There was police everywhere and the road was blocked off. It has shocked the whole community and worried quite a lot of residents too."
The vicar of St Michael's Church, Rector Stephen Potter, said: "At this stage it is hard for me to say how I feel about the incident because I don't know exactly what happened until the police release more information."
A Remembrance Day service at the church was cancelled because the area was cordoned off.
Police have apologised for the cancellation of the service, but said they felt sure the public would understand as 'it was necessary to investigate the death'.
Anybody with information should contact Derbyshire Police on 0845 123 3333.