It took place sometime between 8pm on Sunday 31 December, 2017, and 4.50pm on Tuesday 2 January, 2018, at a house in Stockbridge Road.
Offender(s) forced entry via a ground floor window and carried out an untidy search of the house.
A set of keys was taken and then the occupants’ black Land Rover Freelander was stolen.
An iPad was also taken in the burglary.
PC Paul Farquharson, of Andover police station, said: “We would like to hear from anyone who has any information about what happened.
“Perhaps you noticed suspicious activity in this area over New Year’s Eve and New Year’s Day?
“Have you seen a black Land Rover Freelander in or around the village between the relevant times? Your information could be important to our investigation.”
If you have any information relating to this case, please call 101 quoting reference '44180001974', or contact Crimestoppers anonymously.