Charles Herrmann, an attorney for the family of Antonio Zambrano-Montes, said Thursday that an autopsy conducted by a doctor he hired showed two bullets hit the 35-year-old orchard worker in the back of the arm and in the buttocks.
This is at odds with what police said a day earlier.
Kennewick Police Sgt. Ken Lattin had told reporters on Wednesday, "we do know this from the preliminary autopsy report, there were no shots in the back."
Police said the medical examiner was doing further investigation and a final report might take as long as four weeks. Witness statements and toxicology reports are also pending, police said.
There also is dispute over how many times total Zambrano-Montes was shot. Police said it was five or six times. The family's pathologist said he may have been shot as many as eight times, according to Hermann.
Both sides appear to agree that three police officers fired 17 times at Zambrano-Montes. Police said he hurled rocks at them on February 10.
Zambrano-Montes' case has sparked local protests and anger at what some say is another example of police brutality and excessive force against an unarmed man who is a minority.
Police have alleged that Zambrano-Montes was throwing rocks at cars and trucks when he was confronted by officers. Officers attempted "voice commands and low-level force" and used a Taser, police said, but those efforts didn't work.
After two officers were hit by rocks -- at least one of them as large as a softball -- police said they shot Zambrano-Montes.
Prominent attorney Benjamin Crump, who has represented the families of Trayvon Martin and Michael Brown, announced that he and fellow attorney Jose Baez also represent Antonio Zambrano-Montes' family. Crump and Baez will hold a Friday news conference to disclose the results of an independent autopsy.
Family doesn't believe police
The widow and children of Zambrano-Montes have filed a $25 million claim against the city of Pasco alleging that officers killed the unarmed man "execution style."
In an interview with CNN en Español this week, Zambrano-Montes' mother, Agapita Montes, denounced police treatment of her son.
"I'm asking for justice for what happened. It was not acceptable what they did to my son," his mother said. "From what you can see (on the video), it was very bad what they did to him."
Zambrano-Montes was one of 16 children, his mother said.
Erlinda Zambrano, an aunt of Zambrano-Montes, said she found it very difficult to accept the police version of events.
"We are living with profound pain from how he died, and it's something very bad and terrible," the aunt said. "I look at the videos now and I cannot sleep because it's too hard."
The family lawsuit claims Zambrano-Montes was unarmed "with his hands out where they could be seen."
"He had his back to the officers," the claim said. "At this point, the officers started shooting."
The Tri-City Special Investigations Unit is still reviewing video to see if there was anything in Zambrano-Montes' hand when he was shot.
When processing the scene that night of the fatal shooting, Lattin said at a news briefing, "I think it's safe to say there was a rock found next to his body."
A funeral Mass was held for Zambrano-Montes on Wednesday in Pasco.