Two people were arrested after a car parked outside a house in Killamarsh was believed to have been set alight following a disturbance.
Police were called to the Delves Road area at about 10pm on Monday, January 25 to reports of a disturbance.
A 31-year-old woman was arrested on suspicion of assault occasioning actual bodily harm in connection with the disturbance, while an 18-year-old man was arrested on suspicion of arson in connection with the car fire.
Police want to hear from anyone who might have information relating to the incident.
Safer Neighbourhood officers are in the area performing high visibility patrols and offering reassurance to the community.
Anyone who can help should call Derbyshire police on 101, quoting incident 679 of January 25, or alternatively please call Crimestoppers anonymously on 0800 555 111.