Police attended a house on Acorn Drive, Belper, on the evening of January 2 after receiving a report from East Midlands Ambulance Service that a baby was in cardiac arrest.
The baby was taken to hospital but sadly died last Wednesday.
Following the incident, a 21-year-old woman and a 16-year-old boy were arrested on suspicion of assault and subsequently released on police bail pending further investigations.
On Monday, a Derbyshire Constabulary spokesperson told the Derbyshire Times there were no updates to make people aware of and added: “Enquiries are still ongoing.”
Detectives have been in the area carrying out enquiries into the circumstances which led to the baby’s death.
Flowers have been laid at the scene in tribute to the baby and many people have told of their shock at the incident.