According to prosecutor Åse Schoultz, the employer's possible responsibility as a result of the incident is being investigated.
The classification is work environment crime through negligence to another's death, or work environment crime involving negligence to another's death, says Schoultz to the newspaper.
It is unclear whether the investigation covers the entire Region Gävleborg or only the unit where the ambulance nurse worked.
A man in his 25s, who was arrested at the scene and detained shortly afterwards, was remanded in custody on Monday on probable cause suspected of murder.
The man suspected of the attack had only two days earlier threatened the staff of another ambulance.