The Investigation Discovery show, "My Brother the Serial Killer," will air Wednesday.
The film is a look at Glen Rogers, who was convicted by a Florida jury in 1997 for killing a woman.
Rogers was also convicted of murder in California and is a suspect in homicides in several other states.
Rogers, who is from Hamilton, Ohio, met Nicole Brown Simpson in 1994 when he was living in Southern California, his family says in the documentary.
A criminal profiler in the film says he received paintings by Rogers with clues possibly linking him to the 1994 murders of Simpson's ex-wife and her friend, Ronald Goldman.
Simpson was accused in those killings but the so-called "trial of the century" in Los Angeles ended with his acquittal in 1995.
Simpson never testified at the criminal trial, but memorably demonstrated in court that a glove found near the slaying scene did not fit his hand. He testified at length in a wrongful death trial that led a Los Angeles civil court jury in 1997 to find him liable for damages in the case.
Much of the film is narrated by Rogers' brother, Clay Rogers, who used to rob homes with Glen Rogers as a teen but in 1993, called police on his brother after finding a body at the family's Kentucky cabin.
Clay Rogers said that in 1994, his brother told him about meeting Nicole Brown Simpson.
"They've got money, they're well off and I'm taking her down," Clay Rogers recalls Glen Rogers saying.
Other family members also said Glen Rogers talked about meeting Simpson's ex-wife.
In a statement, Goldman's sister criticized the new documentary.
"I am appalled at the level of irresponsibility demonstrated by the network and the producers of this so-called documentary," Kim Goldman said. "This is the first time we are hearing about this story, and considering that their 'main character,' Glen Rogers, confessed to stabbing my brother and Nicole to death, you would think we would be in the loop."
Simpson is currently serving a prison sentence in Nevada after being convicted in 2008 of leading five men, including two with guns, in a September 2007 confrontation with two sports memorabilia dealers and a middleman at a Las Vegas casino-hotel.