Tia the dog was inside the red Nissan Juke 4x4 vehicle, registration number YK11 GKN, parked in Boroughgate, Otley, when it was stolen at 1.30pm on September 3.
Her owner briefly left the vehicle, and as she returned saw a man had got inside. He initially put the car in reverse, hitting a parked vehicle behind, before driving off from the scene.
The man is described as white, aged in his late 20s, with dark hair, wearing a grey hoody with writing across the front.
West Yorkshire Police have released a number of pictures of Tia and are appealing for the car thief to hand her in.
Pc Joanne Lockwood, of Otley Neighbourhood Policing Team, said: “Understandably, Tia’s owner is extremely upset and concerned for her pet’s welfare. We have been conducting extensive enquiries but at this stage both the vehicle and Tia are still outstanding.
“It may well be that given Tia’s size, the man who stole the vehicle was not aware that she was inside and we would urge him to search his conscience and hand her in.
“If anyone saw any part of this incident or has information about the current whereabouts of the stolen vehicle or Tia the Teacup Chuhuahua then I would urge them to call Otley Neighbourhood Policing Team on 101 or Crimestoppers anonymously on 0800 555 111.”