The way police dealt with three incidents involving a married couple prior to the fatal shooting of the wife is to be investigated.
Caroline Parry, 46, was shot dead in Newport on Thursday. Her husband Christopher suffered gunshot wounds.
The Independent Police Complaints Commission (IPCC) said it was looking into whether Gwent Police had linked three call-outs between May and July.
Police say it is too early to speak to Mr Parry, 49, who remains critical.
On Thursday, Gwent Police's armed officers were called to Seabreeze Avenue at 08:45 BST where the pair were found with serious injuries.
Neighbours reported hearing three gunshots before finding the couple lying on the ground.
Both were taken to the Royal Gwent Hospital where Mrs Parry later died.
At the weekend police said officers had removed three firearms which were "legally held" by Mr Parry from their former marital home in the Cwmbran area.
It is understood Mrs Parry had recently moved out of her home in Croesyceiliog, and was living in Newport.
Their relationship problems had been known to Gwent Police.
As part of its inquiry, the IPCC said it would be looking at what action the Gwent force took in relation to Mr Parry's firearms licence following the earlier incidents.
IPCC Commissioner for Wales Tom Davies said: "This is a tragic incident and a woman has lost her life.
"We will be arranging to speak to family members and explain what the IPCC will be doing.
"Our investigation will look specifically at three incidents between May and July that the police were involved with to establish how they were risk assessed and how Gwent Police officers dealt with them and whether it had linked the incidents.
"Mr Parry held a firearms licence and our investigation will also seek to establish what police action was taken in relation to his licence for shotguns following the reports of the earlier incidents.
"There is an ongoing criminal investigation into the shooting and while this will take priority the IPCC will progress its investigation as quickly as we can."
On Monday, police said it was still too early to speak to Mr Parry who was critically injured with gunshot wounds to the head following the incident in Seabreeze Avenue, Newport on Thursday morning.
Mr Parry is now in a critical but stable condition at the city's Royal Gwent Hospital.
Gwent Police said medical specialists will decide when he is well enough to speak with officers.
A spokeswoman for the force said: "His condition has improved slightly and Mr Parry is now described as stable.
"But it's too early to say when our officers will be able to speak to him about last week's events."