Livingstone said the vehicle was seen travelling down Kaimanawa Street from the direction of Tamamutu Street.
He said the police were "following strong lines of enquiry" in the investigation.
"We'd like to thank the public for the information we have received. This information is being assessed as part of our ongoing enquiries.
"There will continue to be an increased police presence in Taupō while we work to determine exactly what happened to Mr Woodford.
"We understand these incidents can be distressing, but please be reassured we will hold any offender/s to account."
Livingstone asked anybody with any information about the vehicle or who saw it to contact Taupō Police Station and ask to speak with the Operation Dell enquiry team.
Information can also be provided to Police on 105, or to Crime Stoppers anonymously.