Humberside Police have named the victim as 30-year-old Shane Gilmer, who lived in Southburn, a rural village near Driffield.
The father-of-three and his pregnant partner Laura Sugden were both found injured at the property after officers were alerted to a disturbance at about 9.20pm on Friday.
A crossbow was found at the house, and police are now examining it to find out if it was used to carry out the attack.
Mr Gilmer, who worked for East Riding Council, died at Hull Royal Infirmary on Saturday.
Ms Sugden suffered non-life threatening injuries, and both she and her unborn child remain in a stable condition.
Police teams including dogs and the force helicopter are searching the area and local woods, and according to reports the village is in "lockdown".
The force is appealing for information to trace 56-year-old Anthony Lawrence - who is also known as Tony Howarth.
Lawrence lived next door to the victims, and was known to them both.
Chief Superintendent Judi Heaton said she believes Lawrence is still in the country, and officers are now trying to establish the motive behind the attack.
Talking about the live investigation, she said: "We will track him down. We have skilled people on the case, who will locate the suspect".
His car - a navy blue Vauxhall Meriva - was found in the nearby vicinity.
Appealing to Lawrence directly, Chief Inspector Andy Parsons urged him to go straight to his nearest police station, saying: "Avoiding speaking to us could only make matters worse for you in the long run."
The force said it was supporting Mr Gilmer's family during this "difficult and sad time", adding that "the investigation to find the person responsible is ongoing".
Police, who say Lawrence is known to them, are appealing for anyone who believes they have seen him to call them immediately.
Chief Inspector Parsons said: "While we still believe this was an isolated incident and there is no threat to the wider public, please do not approach him yourself."
Officers are now making house to house inquiries, and there will be an increased police presence in the area over the next few days.
Lawrence is described as white, around 5ft 10in tall, balding with short dark hair and of large build.
Witnesses or anyone with information are asked to dial 999.