A car was torched during a break-in at a business unit in Alfreton.
Intruders broke into Meadow Lane Industrial Estate and set fire to a Ford Fiesta which had been parked outside one of the units.
Part of the building was also targeted by arsonists and Derbyshire Fire and Rescue Service attended to deal with the blazes.
The incidents took place between 2.50am and 4am on June 26.
A Derbyshire Constabulary spokesman said: "We are investigating the circumstances surrounding the fires and want to speak to anyone who might have seen suspicious activity in or around the industrial estate.
"Did you see people in the area late at night or do you have information you think could help?
"Witnesses or anyone with information should call PC Andrew Brooks on 101, quoting reference 17000271688, or call Crimestoppers on 0800 555 111."