A 52-year-old grandfather thought to have wounded a "girlfriend" before shooting himself dead did not have a gun licence, police have said.
Mark Osler is thought to have committed suicide 18 months after being given a suspended prison sentence after admitting putting a former partner "in fear of violence".
Detectives are continuing to investigate the shooting incident - during which a month-old baby also suffered a bump to his head - in Feltwell, Norfolk, on Monday.
Mr Osler, a divorced father of three, is thought to have shot 40-year-old Rachel Puttock in the head outside his home in Feltwell with a pistol - then turned the gun on himself. Police said Ms Puttock was recovering in hospital.
Ms Puttock's grandson, Owen, is thought to have banged his head when he fell from a pram during the incident.
Mr Osler, who had two teenage sons, and a son in his 20s, had appeared before a judge at Norwich Crown Court in January 2009 after attacking an ex-partner.
A local newspaper report said Mr Osler had assaulted the woman three times in less than a year - once pouring cola over her head as she sat in a pub. He was given a nine-month prison sentence suspended for 12 months.