The incident took place on Wednesday evening.
An Audi TT was seized at a Brimington petrol station on Ringwood Road last night.
Officers tracked the vehicle at around 9.30pm last night due the manner in which it was being driven.
They later discovered the driver was both uninsured and without a licence, whilst the vehicle had previously been involved in the theft of fuel.
The passenger, a 41 year old man from Staveley, was given a fixed penalty notice for not complying with Covid-19 restrictions.
Brimington, Chesterfield. Audi TT with a marker on it as involved in theft of fuel, seen filling up with fuel. Paid today's bill but he hasn't got a licence or insurance. Ticket and seizure of car for him, COVID restriction breach ticket for the passenger. #Traffic #Seized #Crime pic.twitter.com/PwgrjV97Ph— Derbyshire Roads Policing Unit (@DerbyshireRPU) May 7, 2020