On May 1st the girl, called Yara by the Swedish media, was discovered in a grievous condition at an apartment in Landskrona. She subsequently died in hospital and her two guardians have since been remanded on suspicion of murdering the 8-year-old.
Now the police are being investigated after it emerged that a neighour had alerted the authorities with suspicions that the girl was being abused.
On Good Friday, she met the 8-year-old in the elevator of their apartment building and noticed that she was bruised and had problems walking. The police sent the complaint on to social services four days later, as the report coincided with the long Easter holiday weekend.
IN PICTURES: Karlskrona in mourning over tragic death of 8-year-old girl
The new investigation centres around the action that was taken when the original notification was received.
"The reason the preliminary investigation has been initiated has to do with the official measures taken," prosecutor Mats Åhlund told the Blekinge Läns Tidning.
The paper added that the notification stated the policeman was suspected of neglecting his duties when the report was lodged on April 18th.
He has since been assigned a public defender and the case is ongoing.
A fortnight after the girl's death the principal of a school in Karlskrona was suspended after failing to act on the signs that she was being abused.
The deceased girl came to Sweden by herself last year. The 31-year-old man and the 30-year-old woman, who were recently remanded in custody suspected of probable cause for murder, were her legal guardians.
The girl's parents found out about her death via Facebook, before the authorities in Sweden managed to liaise with police in Gaza to try to have an officer tell the family of the death in person.