The break-in happened at a property in Thornhill Road, Rastrick, at about 6.30pm on January 15.
The suspect, who was with a second man, entered the home while the occupant was asleep.
But they were disturbed and fled the scene after the man inside, in his 50s, woke up.
Police today issued an E-Fit image of a man they are trying to trace in connection with the break-in.
Detective Constable Jason Mohan, of Calderdale CID, said: “Clearly this has been a distressing experience for the victim and I would appeal to anyone who has any information about the incident, or who can identify the suspect in the E-Fit to come forward.
"Enquiries are ongoing into the incident.”
The suspect pictured is described as a white man, about 5ft 11ins tall, and around 20 to 26-years-old.
He is described as being of a slim, athletic build, with light blonde hair, and was wearing a grey zip up jacket with a red collar, grey tracksuit bottoms and white trainers.
Anyone with any information is asked to contact police on 101, quoting 13180024487.
Information can also be passed to Crimestoppers anonymously and in confidence on 0800 555 111.