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Natalie Hemming disappearance: Search for red rug in missing mum case
Ms Hemming was last seen in Hemel Hempstead, Hertfordshire, at about 15:00 BST on 1 May and was reported missing by a relative on 3 May.
On Wednesday, officers scoured an area around Salden Wood near Newton Longville in Buckinghamshire and a disused railway line, both near the family home.
The force said the rug, described as 12ft by 10ft with a 3in soft pile, was discovered to be missing during a search of the house.
Det Supt Chris Ward said: "Anybody who has seen a similar rug discarded anywhere, particularly within Aylesbury, Oxford, Milton Keynes or over the border in Bedfordshire, [or who has] has seen it, picked it up or moved it [should] to speak to us as soon as they can."
He said the force's main objective was to find Ms Hemming and return her to her family.
"There are a number of searches going on both within the Thames Valley Police area to the east of Milton Keynes and in the Bedfordshire area as we follow up the information that we've had," he said.
"This has, very sadly, become a murder investigation and detectives will be making ongoing enquiries in relation to it."
Officers are also trying to trace the movements of a black Ford S Max - registration EJ12 UWG - that could be connected with Mrs Hemming's disappearance.
It is believed to have travelled on the A413, the A418 and the A41 around Aylesbury, between 21:45 on 1 May and 00:45 on 2 May.