Emergency services descended on the house in Newby Crescent in the early hours yesterday after reports of two people being bitten by a dog.
The American Pit Bull had bitten a 39-year-old man and seriously injured a 40-year-old woman, who was trapped in the upstairs bedroom.
The dog was on the loose downstairs and had tried to bite others.
When it became apparent that the dog could not be brought under control, it was shot by a firearms trained officer.
A North Yorkshire Police spokeswoman said they were called to reports of a dog injuring several people at around 1.15am.
She said: “The dog was extremely aggressive and still in the property when officers arrived. The injured woman was also still inside the property.
“Efforts were made to try and control the dog in order to reach the woman, who was in need of urgent medical assistance.”
She said it became clear at around 1.40am that urgent action was needed.
“A firearms trained officer was required to swiftly resolve the incident, which has resulted in the destruction of the American Pit Bull type animal.”
Both victims were given treatment for their injuries.
Crews from Harrogate Fire Station had joined police at the scene shortly before 1.30am but were not asked to take action.
A full police investigation into the circumstances surrounding the dog attack as now begun.