Police have been given more time to question a man in his 20s, who was arrested in connection with the murder of PCSO Julia James.
Ms James, a popular community support officer, was found dead in Akholt Wood near her home in Snowdown, Kent, on April 27.
The 53-year-old died from serious head injuries while out walking her dog Toby, who was found unharmed by her side.
The man, a British national who is from the Canterbury area, was arrested at 9.30pm on Friday night, and remains in custody, Kent Police said.
They have now been granted an extra 36 hours to question him. The extension lasts until Monday evening.
On Wednesday, police issued an image of Ms James in the clothes she was wearing before she was killed.
The picture shows Ms James walking her Jack Russell, Toby, while wearing a light blue waterproof coat, blue jeans and dark Wellington-style brown boots.
Police said it was the same clothing, apart from the gloves, which she wore on the day she died.
A search is taking place at a property in Sunshine Corner Avenue, Aylesham, which is linked to enquiries being made in relation to the murder, police have said.
Assistant Chief Constable Tom Richards from Kent Police said: "We continue to urge anyone with information, no matter how small or insignificant it may seem, to contact us.
"If you were in the Snowdown area between 1pm and 4.30pm on Tuesday April 27 please contact us.
"This includes anyone local who may have seen something out of place at the time, or who came across someone who made them feel uneasy – such as feeling compelled to cross the road or change the route they were walking."
Kent Police had released a photo on Friday of a man they said could be of "crucial importance" to the investigation.
But the force said the man had been identified and that they were no longer appealing for information about him.
Crimestoppers has offered a reward of up to £10,000 for information that leads to Ms James' killer being convicted.
Anyone with information is urged to contact Kent Police on 0800 0514 526. Witnesses and anyone with any information, CCTV or dashcam footage are also asked to submit details online via this link.
You can also contact Crimestoppers on 0800 555111, or by using the online form.