Cumbria Police said officers were called to an address on Hartington Street in Barrow-in-Furness at 6.30pm on Tuesday following reports of a man causing a disturbance.
A Taser and pepper spray were used during the arrest of 27-year-old Dale Burns, who later died in hospital.
A police spokesman said: “Neighbourhood police officers attended the scene and arrested a male on suspicion of causing criminal damage and, during the arrest, a Taser was deployed.
“The man became unwell following the arrest and was taken to Furness General Hospital by officers.
“At around 9pm the man, who was in his 20s and lived locally, was pronounced dead.”
The incident has been referred to the Independent Police Complaints Commission (IPCC). In a statement IPCC Commissioner Naseem Malik said “I would like to extend my condolences to the family of Mr Burns at this difficult time… A taser and spray was deployed during the arrest and we will be examining whether the actions of police officers were proportionate in the circumstances and in accordance with police procedures.”
Taser stun guns deliver an electric shock designed to disable a suspect without causing long-term injury.
They are allowed to be used in situations where firearms officers are authorised to carry their firearm, or when the officer believes the suspect is displaying threatening behaviour.
But human rights groups have campaigned against their use by British police forces as the weapons have been linked to dozens of deaths in north America.
The last person in Britain to die after being Tasered was Brian Loan, 47, from Sacriston, County Durham, in October 2006. An inquest into his death ruled he had died of heart problems.
The IPCC has said it is awaiting the results of a post mortem on Mr Burns to establish the cause of his death and has asked for patience from the public while it “seeks to gain answers to the to the questions understandably raised.”