The case is the focus of Making a Murderer, the popular – and controversial – docu-series on Netflix.
Avery is currently serving life in prison without the possibility of parole. His nephew, Brendan Dassey, is also in prison for his alleged role in the murder. (Dassey will first meet the parole board in 2048.)
For their part, police and prosecutors tell PEOPLE that the right men are in prison.
If Avery and Dassey didn't kill Halbach, who did? In post-conviction court documents obtained by PEOPLE, Avery has pointed the finger inside his own family, claiming that his brothers – who have never been charged in connection with the murder of Teresa Halbach – could be suspects. (Calls to Avery's brothers have not been returned.)
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Charles AveryThe 59-page document alleges that Steven Avery's brother, Charles, had a history of strange behavior against women, including women who had visited the Avery Salvage Yard, the family's auto salvage business. In one 2005 police report from the Calumet County Sheriff's Department, he allegedly paid unwanted attention to a woman whose car he had towed. "She reported to her co-workers that she was afraid of him," the police report states.
Also according to the document, Charles Avery was charged in 1999 with sexual assault by use of force on his then-wife. (PEOPLE has independently verified the arrest.) Charles Avery was not convicted and his wife later dropped the charges.
According to the court document, Steven Avery believed that Charles had a reason to “frame Steven over money, a share of the family business, and over [Steven's former girlfriend] Jodi Stachowski."
Earl AveryThe document also alleges similar behavior from Steven's other brother, Earl Avery.
According to the document, Earl Avery was charged with sexually assaulting his two daughters in 1995. (He pleaded no contest.)
The documents claim that Earl Avery was "hunting rabbits" on the day that Halbach was murdered – and that he later drove his golf cart past her car on the salvage yard.
"Both Earl and Charles Avery would have known more about the Avery Salvage Yard than anyone else," says the document.
"They had taken over the day-to-day running of the business. They had the means and the opportunity to kill Ms. Halbach, to move her car, to plant evidence to incriminate Steven, and then to leave the car so that it would be discovered in a search."
Scott TadychAt the time of the murder, Scott Tadych was dating Brendan Dassey's mother, Barb Janda, who lived next door to Steven Avery.
According to the document, "Tadych's motive to kill Ms. Halbach is his violent and volatile personality. According to Tadych's co-workers, he is a short-tempered and angry person capable of murder. Tadych was described as a chronic liar who blows up at people, 'screams a lot' and is a 'psycho.' Another co-worker described Tadych as 'not being hooked up right.' "
To corroborate Avery's claim, he listed Tadych's multiple arrests for criminal trespass, disorderly conduct, and battery. (PEOPLE has independently confirmed the four cases against Tadych, in 1994, 1997, 1998 and 2002, as well as a 2001 temporary restraining order filed by an ex-girlfriend.)
Tadych was a witness against Avery during the trial and has never been considered a suspect in the murder.
Bobby DasseyThe fourth person named as a possible alternative suspect was Avery's nephew, Bobby Dassey.
Although Bobby Dassey didn't have a history of violence, the documents claim that he "also had the opportunity, as he was at home at the time that Ms. Halbach was on the property. Given that Ms. Halbach was coming to photograph his mother's car, Bobby would have known that Ms. Halbach was coming to the property. Bobby admitted that he saw Ms. Halbach and her car as he looked out the window. He had the means to shoot Ms. Halbach; he is a hunter and thus would have access to weapons.
The document continues, "Thus, there is circumstantial evidence tying Bobby Dassey to Ms. Halbach's murder."
The document, filed in 2009, sought to have Avery's conviction overturned. The court disagreed, and denied the appeal.
None of the "suspects" Avery put forth have been connected with the murder of Teresa Halbach.