The police watchdog is investigating why the man who shot dead five people in Plymouth had been given back his confiscated gun and permit.
Jake Davison was stripped of the weapon and its licence in December after he was accused of assault, the Independent Office for Police Conduct (IOPC) says.
It is to examine why Devon and Cornwall Police decided to return them in July.
Home Secretary Priti Patel has paid her respects to the victims by placing a floral tribute near the scene.
She laid the bouquet at North Down Crescent Park, where hundreds of people attended a vigil on Friday evening. Chief Constable of Devon and Cornwall Police Shaun Sawyer also laid a bouquet.
The home secretary and Plymouth Sutton MP Luke Pollard then spoke with members of the local neighbourhood watch team at the park.
"It's tragic beyond words, really, really tragic, for a range of reasons, and obviously for those involved," Ms Patel told them.
"I'm sure everyone will have known each other and this really will have touched so many people's lives."
On Thursday evening, Davison, 22, shot his 51-year-old mother Maxine Davison, also known as Maxine Chapman, at a house in Biddick Drive. He then went into the street and shot dead Sophie Martyn, aged three, and her father Lee Martyn, aged 43.
He killed Stephen Washington, 59, in a nearby park, before shooting Kate Shepherd, 66, on Henderson Place. She later died at Derriford Hospital.
Davison also aimed and shot at two local residents - a man aged 33 and a 53-year-old woman - who are known to each other, in Biddick Drive.
His attack, in Keyham, lasted about six minutes before he turned the gun, described by witnesses as a pump-action shotgun, on himself.
Prior to the shooting, Davison had posted hate-filled online rants about single mothers and about his own mother in particular, calling her "vile, dysfunctional and chaotic".
The IOPC said it had launched an investigation on Friday evening after it received preliminary information that Davison's firearm and licence were returned to him in early July this year.
The certificate and shotgun had been removed from him by police in December 2020 following an allegation of assault in September 2020, the watchdog said.
Prime Minister Boris Johnson had earlier said the issue of how Davison came to legally own a gun should be "properly investigated", adding that the shooting was an "absolutely appalling" incident.
Regional IOPC director David Ford said: "We will examine what police actions were taken and when, the rationale behind police decision-making, and whether relevant law, policy and procedures were followed concerning Mr Davison's possession of a shotgun."
It will also look at whether the force had information concerning Davison's mental health and if this was "appropriately considered".
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