The payment includes $200,000 for Salt Lake City attorney Jesse Trentadue.
The ruling came out of the family's battle over the 1995 death of Kenneth Trentadue, an ex-convict who was found dead in a federal prison in Oklahoma hanging from a noose made of torn bed sheets. Prison officials say the 44-year-old inmate, who was in custody on an alleged parole violation, committed suicide.
The Trentadues, though, believe he was murdered and they sued the government.
U.S. District Judge Tim Leonard of Oklahoma ruled in 2001 that Kenneth killed himself but awarded family members $1.1 million for the emotional distress caused by the way prison officials handled the case. The government appealed.
Last year, the 10th U.S. Circuit Court of Appeals in Denver said the Trentadues suffered a terrible shock when they saw the prisoner's battered body in a funeral home. In addition, the court agreed that the horror was magnified by the failure of correctional officials to warn the relatives that an autopsy had been performed on Kenneth's body, something they discovered when they saw incisions from the procedure.
However, the 10th Circuit sent the case back to Leonard to assess the severity of the emotional distress of each family member. In Monday's ruling, the judge wrote that "the extreme and outrageous character of the defendant's conduct is important evidence that the distress existed."
The award money will go to Kenneth Trentadue's widow, mother, two brothers, sister and the estate of his late father.
Jesse Trentadue said he is happy but saddened that Chuck Sampson, his law partner who argued the case, died this summer before the decision was issued.
"This may be the only instance where the U.S. government has been found guilty of intentional infliction of emotional distress," Trentadue said.
The attorney is pursuing a theory that his brother, who had served time for bank robbery, was killed during an interrogation that got out of hand. He thinks authorities mistakenly believed Kenneth Trentadue was part of a gang that robbed banks to fund attacks on the government, possibly including the Oklahoma City bombing that killed 168 people.
A hearing on his suit seeking records on the case from the FBI is scheduled for next month in Salt Lake City.