Humberside Police have named the victim as 30-year-old Shane Gilmer, who lived in Southburn, a rural village near Driffield.
Mr Gilmer and a woman were found injured at the property after officers were alerted to a disturbance at about 9.20pm on Friday.
According to reports, a crossbow was used in the attack and the village is in “lockdown”.
Mr Gilmer died at Hull Royal Infirmary on Saturday, while the woman, who has not been named, remains in a stable condition.
Police teams including dogs and the force helicopter are searching the area and local woods.
The force is appealing for information to trace 55-year-old Anthony Lawrence following the attack.
His car – a navy blue Vauxhall Meriva – has been found.
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”.
Chief Inspector Andy Parsons said: “We are still appealing for anyone who believes they have seen Mr Lawrence to call us immediately.
“While we still believe this was an isolated incident and there is no threat to the wider public, please do not approach him yourself.”
Mr Lawrence is described as white, around 5ft 10in tall, with short dark hair and of large build.
Witnesses or anyone with information are asked to dial 999.