Julia James was working from home on Tuesday and was last seen leaving to walk her dog in the afternoon. She was not in uniform.
Her body was found in Akholt Wood, Snowdown, near Dover, later that day.
Police said Ms James died from “significant head injuries” as a result of “blunt trauma” and that they are “working very hard” to identify a motive for the killing.
There was no evidence that any of her possessions were missing and her dog was found unharmed at the scene when police arrived.
People should be “cautious, vigilant, aware of their surroundings”, Kent Police assistant chief constable Tom Richards said on Friday morning.
Tim Smith, Kent Police’s deputy chief constable, said hundreds of officers were on the investigation into her death but there were currently no “clear suspects”.
“We’ve got hundreds of officers working on that investigation while we try to establish exactly what happened to Julia, and more importantly who did this to Julia and why,” he told BBC Radio Kent.
“We’re working very hard to identify a motive and we are working very hard to identify who may have committed this.”
DCC Smith said he was “not able to say either way” if the attack was sexually motivated, adding that police “keeping a very open mind about the motive”.
The death was originally viewed as “suspicious”, but Kent Police confirmed on Wednesday afternoon that it is being treated as murder.
Ms James’s nephew Karl James said his aunt was “just a lovely person” and said her death has been “a real shock”.
Speaking to 5 News, he said: “Obviously it’s been a real shock. I work away, but my wife is here – heavily pregnant – and with young kids, so she’s on edge at the moment too.
“So I’ve come home and just waiting for answers – that’s the worst bit really.”
Floral tributes have been left for Ms James, who had worked for the police for nearly 15 years, in nearby Aylesham.
Officers have appealed for anyone who may have seen something unusual or suspicious in the area on Tuesday or Wednesday to come forward.
They are encouraged to contact Kent Police on 0800 0514 526.