Cleveland Police did not name the suspect they are seeking following the discovery of a body at an address in Cherwell Terrace, Bramble's Farm, Middlesbrough, at 1am.
A force spokeswoman said:
The man police are trying to trace in connection with the incident is believed to be white, in his 40s, around 6ft 2in tall and of proportionate build.
He has short, dark brown hair and was last seen wearing a chequered shirt, dark jeans and black trainers.
Police believe this has been a targeted, domestic-related incident. However, they are appealing for anyone who has seen this man or knows of his whereabouts, not to approach him directly but to get in touch with Cleveland Police via 999.