The mother and one child in the family died in the crash, which took place at a campsite in Färjestaden.
The 56-year-old driver is suspected of grossly causing another person's death, grossly causing bodily injury, causing danger to another and gross negligence in traffic.
Major forensic psychiatric examination
The 56-year-old was initially requested to be detained, but Kalmar District Court decided that he should be released and undergo a minor forensic psychiatric examination.
According to it, the man may be suspected of having suffered from a serious mental disorder both at the time of the incident and at the time of the investigation, reports Kvällsposten.
The doctor in charge believes that there is reason to have him undergo a major forensic psychiatric examination.
The man has denied the crime and claimed that he does not remember what happened.
Prosecutor Kjell Janneson tells the newspaper that prosecution can hopefully be brought before Christmas.