The 48-year-old died 90 minutes after he was hit by the stun gun in the street where he grew up in the Trench area of Telford, Shropshire, in the early hours of Monday.
According to relatives Mr Atkinson was suffering from a number of health issues and had a weak heart when he was hit by the weapon at around 1:30am.
The retired sportsman went into cardiac arrest in an ambulance on his way to hospital and medics were unable to save him. The death is now under investigation by the Independent Police Complaints Commission (IPCC), the police watchdog who investigate all instances when a Taser is used.
Mr Atkinson’s brother, Kenroy, 53, said the ex-Premier League star had undergone dialysis for kidney failure and was “not in his right mind”. He said his brother had attacked their 85-year-old father, Ernest, at his home before police were called to the scene.
“My brother had lost it. He was in a manic state and depressed – out of his mind and ranting. He had a tube in his shoulder for the dialysis and he had ripped it out and was covered in blood,” he told the Sun newspaper.
“He got Dad by the throat and said he was going to kill him. He told Dad he had already killed me, our brother Paul and sister Elaine and he had come for him.
“We are all devastated. Our family is heartbroken.”
The shock delivered by a Taser can be thousands of volts in strength and is intended to immobilise.
Mr Atkinson’s nephew, Fabian Atkinson, suggested officers would not have used the stun gun if they had known the ex-striker’s medical history.
He said: “When a Taser is deployed, as soon as a Taser is deployed, they need to automatically call an ambulance. How do they know the health of the guy or the girl that they are affecting?”
West Mercia Police said officers were called amid concerns “for the safety of an individual”.
Mr Atkinson was a top-flight striker in the 1990s, starting his career at Ipswich Town then playing for Sheffield Wednesday and Spanish side Real Sociedad before moving to Villa. He scored 23 goals in 85 appearances for the Birmingham side between 1991 and 1995. He ended his playing career in South Korea in 2001.
Police use of Tasers, which are intended as a non-lethal weapon, went up slightly last year with 10,329 uses by forces in England and Wales, a 2 per cent rise on the previous year.