The Saab was stolen from a house on Green Lane, Sowerby, at approximately 2.40pm on Friday 30 March 2012.
The suspect entered the house through an unlocked door before searching the property and stealing the car keys.
The Saab 93 is a blue convertible and Its registration number is YK07SZP.
It believed the same man approached a house on Grey Close, Sutton on the Forest, near York on Monday 9 April 2012. He left the address when he was challenged by a neighbour.
Detective Constable Chris Burton said:
I ask anyone who witnessed the theft or can help to identify the man to come forward and contact the police straight away.
It is possible that the man was a genuine caller to the house in Sutton-on-the-Forest. If this is the case, I ask him to contact the police so we can eliminate him from our enquiries.
Anyone who can help the police with their enquiries is asked to contact on 101, press option 2 and ask for Chris Burton.
Alternatively call Crimestoppers anonymously on 0800 555 111 quoting reference number 12120050350.