But it has now emerged that the girl's 28-year-old father - who for a short time was considered to be a suspect - brought her to the hospital on Tuesday after she had vomited repeatedly and slept far more than usual.
He was told to come back on Wednesday. But even on Wednesday he was sent home by doctors.
On Thursday the baby's condition became worse and her father rushed her to the hospital in a taxi in the evening. Doctors confirmed that she was dead on arrival at Karolinska.
According to the man's lawyer, Johan Eriksson, the doctors reported the father without there being any medical grounds for suspecting that he had killed his daughter.
"It was a feeling or something which made them do it. I believe the doctors reacted to something in his behaviour at the hospital and reported him to be on the safe side," said the lawyer.
As a result, the father was arrested after being charged in his absence. During Saturday's preliminary hearing, prosecutor Eva Wintzell accused him of manslaughter.
He was accused with 'reasonable suspicion' but after an hour-long hearing he was released without charge.
"There was nothing to indicate that any crime had occurred," said detective Ingmarie Multén at west Stockholm police to Svenska Dagbladet.
But prosecutor Eva Wintzell told TV4's Nyheterna programme that the father is still under suspicion. According to her, the cause of death is still unclear.
"You can't say that there has been a crime or that there hasn't been a crime," she said.
The results of forensic tests carried out on the girl are due in a couple of weeks.
Johan Eriksson spoke to his client on Monday:
"He wants to know why his child died. Of course, he's asking whether there was something the hospital staff could have seen when he was there on Tuesday or Wednesday."
"Right now he feels outraged at having been a suspect and spending two days in a police cell instead of being with his family and mourning under normal conditions," added Eriksson.
The medical investigation indicates that the girl had an infection, according to Johan Eriksson. He and his client will discuss the possibility of taking legal action against the hospital in due course, he said.
Karolinska hospital would not comment on the case, but a decision about whether there will be an internal investigation into possible negligence will be made later this week.