The force is appealing for dashcam footage from Roemead Road, Roemead Lane, Simbriss Road, Pound Lane, Galley Batch Lane and Golf Links Lane from between 18:00 on 1 January and 02:00 on 2 January.
Officers are also keen to view dashcam footage from Roemead Road from 23:00 GMT 30 December until 02:00 on 31 December.
CCTV, forensic, and house-to-house enquiries have been carried out, the spokesperson said.
Chief Inspector Karen Corrigan said dashcam footage “will be crucial” to the investigation.
“We are working with our colleagues at Wiltshire and Dorset Police, and Craig’s family are being offered support,” she said.
“We are remaining open-minded about the circumstances surrounding Craig’s disappearance.”