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 in the attack.
Mr Gilmer, who worked for East Riding Council, died at Hull Royal Infirmary on Saturday.
Ms Sugden suffered serious but non-life threatening injuries, and both she and her unborn child remain in a stable condition in hospital.
According to reports the village is in "lockdown", and police teams including dogs and the force helicopter have carried out an extensive search of the area and local woods.
The force is appealing for information to trace 56-year-old Anthony Lawrence - who is also known as Tony Howarth.
Chief Superintendent Judi Heaton said: "We don't want the public to approach him. He's a suspect in a murder case and he's also wanted for the attempted murder of a pregnant lady at their home."
Lawrence lived next door to the victims and was known to them both.
Officers believe he is still in the country.
They are now trying to establish a motive behind the attack.
His car - a navy blue Vauxhall Meriva - was found nearby.
Talking about the hunt for Lawrence, CSI Heaton said: "We will track him down. We are working long and hard and we have some very skilled people working on the case, who will locate him."
Appealing to Lawrence directly, Chief Inspector Andy Parsons urged him to turn himself in: "Avoiding speaking to us could only make matters worse for you in the long run."
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 enquiries, 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.
