A month-old baby girl died during the early hours of Saturday after suffering a cardiac arrest at the family home in Corsham.
A fast response ambulance car was sent to the home in Corsham after a 999 call was made at around 4am.
A spokesman for Wiltshire Air Ambulance said: “It was a very sad case.”
Police were also called to the child’s home just before 5am.
A spokesman said: “We had a call to say a small child had suffered a cardiac arrest.
"The baby and mother were taken to the Royal United Hospital, Bath, but the baby died.”
A spokesman for the Wiltshire Coroner said they were unable to give any details at present about an inquest opening as they were waiting for a report from the Avon coroner.