Michael Atherton shot his partner Susan, her sister Alison and 24-year-old niece Tanya before taking his own life at his home in Peterlee last year.
An inquest into their deaths began today and heard that a note had been attached to Atherton's request for a shotgun license in 2006 which said:
"Four domestics, last one 24/4/04, was cautioned for assault.
"Still resides with partner and son and daughter.
"Would like to refuse, have we sufficient info to refuse re public safety."
However, Atherton was still granted a shotgun certificate then and a firearms licence two years later.
The inquest also heard that there was no formal training for police officers involved in the granting of firearms licences.
Witness B, who cannot be named, said:
"There was no formal training, I'm not aware of any formal training in firearm departments.
"Ninety percent of application forms were straightforward."
Evidence was also given by pathologist Dr Nigel Cooper who said Atherton had about one and half times the alcohol driving limit in his blood at the time, which was the equivalent to a few drinks.
Atherton had previously had his guns confiscated after threatening to shoot himself when drunk.
The coroner has ruled that the deaths of three members of the same family, and their shooter, could have been avoided.
An inquest has heard how a man who went on to kill three members of his family before turning the gun on himself had been warned by police.
The inquest into the deaths of a man who shot himself and three members of his family on New Years Day 2012 has been taking place today.