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A policewoman called to reports of a disturbance was left injured after trying to stop a car fleeing.
The constable was one of two officers sent to an address in West Street, Gillingham.
As one of them spoke with the occupant of the property, three men were seen leaving through a back door.
They headed down a path and got into a blue Audi A3 in Crown Street – a fourth man was in the driver’s seat.
The officers approached but as they leaned in to ask the occupants to stop, the car drove away.
The PC fell to the ground – suffering a cut arm and grazing to her legs.
Now detectives are appealing for information as they bid to catch the culprits.
One of the men was white, in his late 20s to early 30s, around 5ft 10ins, of average build and had black hair.
A second man was white, around 5ft 10ins, with a large build and short, dark hair. He was also seen wearing a black Nike t-shirt.
The third was in his mid-20s and around 5ft 7ins, slim and short black hair.
It happened at around 10.50pm on Monday.
On Wednesday, a 25-year-old Chatham man was arrested on suspicion of assaulting an emergency services worker.
He has since been released, pending further inquiries.
Investigators are keen to hear from witnesses, especially anyone with privately-held CCTV recorded in the area, or motorists with dash cam who were travelling in the area at the time and have captured a blue Audi A3.
Anyone with information is asked to call 01634 792209, quoting 46/144334/21.
You can also contact the independent charity Crimestoppers anonymously by calling 0800 555111 or using by the anonymous online form.