Kenneth Oliver, 45, of Miami-Dade, was targeted after causing a commotion at a friend’s house.
It is reported he had been shouting and banging on a front door in the early morning.
Mr Oliver’s friend Johnnie Mosely said he had considered letting him into his home, but his daughters were frightened by Mr Oliver’s behaviour.
He called police and said officers, who arrived several minutes later, used a Taser gun at least four times.
Miami-Dade police say Mr Oliver went into shock while he was in custody and was pronounced dead at a hospital later that morning.
Force spokesman Bobby Williams says the death is under investigation.
The use of Taser weapons by police has caused controversy in the US.
- A d v e r t i s e m e n t
In September 2007, a Florida university student was restrained on the ground, Tasered and arrested after asking questions at a political forum.
Earlier this year, it was revealed an American motorist – who became a celebrity after video of him being stunned with a police Taser gun appeared on YouTube – will receive about £20,000 from Utah State.
Jared Massey, 28, was arguing against a speeding ticket when he was shot.