Police are investigating whether the call that led police to the home was a so-called "swatting" prank, in which someone makes up a false report to get a Swat team to descend upon a home.
Such pranks are common among online gamers. Lisa Finch, the mother of the dead man, said he did not play video games.
Lisa Finch told the Wichita Eagle 28-year-old Andrew Finch, the father of two young children, was unarmed when he opened the door to the family home on Thursday night after hearing something.
She said he screamed and was shot.
The family then was forced outside barefoot in freezing cold, she said, her granddaughter being forced to step over her dying uncle. Family members were handcuffed, she said, placed in separate police vehicles and taken in for questioning.