Armed officers were called to Seabreeze Avenue in Newport, south Wales, after neighbours reported hearing three gunshots and then finding the pair lying in the road.
A gun was later recovered from the scene.
Detectives said the two people involved had previously been in a relationship, which had “come to the attention” of police in the past.
Chief Inspector Huw Nicholas, of Gwent Police, said yesterday the force was still trying to establish exactly what happened but at present they were not looking for anyone else in connection with the incident.
“While I am limited as to what I can say about the people involved, what I can say is it is known that they had previously been in a relationship which had come to the attention of police,” he added.
“For this reason we have referred the matter to the Independent Police Complaints Commission (IPCC).”
“Our forensic investigators are still at the scene and a team of detectives are working on the investigation.
“Extra officers are in the vicinity, but this is purely from a reassurance point of view.
“Residents are obviously shocked and distressed about this morning’s events and we have officers and Community Support Officers in the area who will be available to speak to residents as required.”
The alarm was raised at around 8.40pm yesterday when a man walking his dog heard gunshots before finding the 46-year-old woman and 49-year-old man lying in the street.
Local resident Sam Williams, 33, said he was shocked by what he saw.
“The woman was close to her car with a fatal shotgun wound to the chest,” he told BBC Wales.
“I called the woman for a response but it was obvious it was too late.
“The man was still alive and breathing.
“There was a single-barrel shotgun and two cartridges on the floor.
“I didn’t want to go too close or touch anything. The lady’s car engine was running but the police told me not to touch anything.”
The couple were then taken to the Royal Gwent Hospital in Newport. The woman died, while the man underwent surgery.
A Gwent Police spokeswoman said: “The 49-year-old male remains in hospital in a critical but stable condition. It is not believed anyone else was involved in the incident.”
Meanwhile, officers said they are particularly keen to speak to anyone in the Seabreeze Avenue or Willenhall Street area between 8am and 10am on Thursday.