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A spokeswoman said: "Police believe this has been a targeted, domestic-related incident."
The scene was heavily guarded by police today and a white forensics tent had been set up in the front yard of the brick-built terrace house.
One woman in a nearby property, who declined to be named, said: "All I saw were lots of blue lights and this morning they said someone had been murdered - a lass, I think.
"It's a good estate - you don't expect this."
Cleveland Police have released a description of Graham Barry Gibson, who they want to trace in relation to the death of a woman in Middlesbrough.
He's believed to be white, in his 40s, 6ft 2in tall, with short dark brown hair. He was last seen wearing a chequered shirt, dark jeans and black trainers.
Police have advised the public not to approach him.
A man wanted over the death of a woman whose body was found at an address in Middlesbrough has been named by Cleveland Police today as Graham Barry Gibson.
The public have been warned not approach him.