The crash happened Thursday evening near U.S. 301 and May Drive.
An eyewitness told ABC11 that she saw the deputy's car flip seven times before coming to rest in the grass off the side of the road. Stone said Friday that it appears Allison's Ford Explorer flipped at least once after he veered to try to avoid another vehicle and struck a culvert.
Stone said Allison, 26, was ejected through the passenger side door. He could not say for sure whether the deputy was wearing his seat belt or whether it snapped.
The sheriff said Allison was "not responsive" at the hospital and added that "we're in prayers for his life."
"Our sheriff's office is like a family; we preach that," Stone said. "It's very difficult, with me being a leader, sending these people out to serve and protect."
Stone said Allison had just completed a traffic stop and was beginning a traffic response after a motorcyclist was driving in a "careless and reckless manner" heading south on U.S. 301.
The white Nissan Maxima involved in the crash with the deputy was not part of the traffic response and was simply a driver making his way along the roads, turning onto U.S. 301, Stone said. He added that the driver was "walking and talking" and not seriously injured.
Rocky Mount Police Department and the North Carolina State Highway Patrol led the investigation into the crash. Stone said traffic reconstruction teams are still working the scene and piecing together what happened.
No charges have been filed. The motorcyclist did not stop and has not been found.
Nash County Sheriff's Office issued a Tweet on Thursday evening asking everybody to pray for those involved in the crash.
A short time ago a member of the Nash County Sheriffs Office was involved in a motor vehicle accident w/ another vehicle on US301 in Rocky Mount. The crash is being investigated by the NCSHP. Please pray for all those involved. No other information is being released at this time— Nash County Sheriff (@NashCountySO) November 27, 2020
Stone called Allison a "phenomenal officer" and said he is married and has a 9-year-old son.