The grey Caddy, registration number YE08 WPX, was stolen by thieves who pulled up in a white van last Wednesday.
The stolen van was driven to an industrial estate in Ryefield Way, Silsden, where the registration plates were replaced with a set taken from a parked vehicle.
The Caddy is now believed to be displaying the number YY12 AYP.
Police are appealing for anyone who has seen the van bearing either of the two plates to contact them.
They also want to hear from anyone who has any other information about the theft. They should call 01904 618691, select option 2 and ask for PC Mark Browne.