According to the report by Press TV, Neda was killed "in an ally away from the scene of clashes."
The network quoted the man who allegedly drove her to hospital as saying her death appeared to be "highly suspicious," as there were no police, Basij militia, or any other Iranian security forces nearby.
Verifying the details of Press TV's report is impossible as Iran's hard-line rulers have expelled almost all foreign news staff from the country and cracked down hard on any voices of dissent in the wake of the disputed June 12 election.
"People were standing, there was traffic and people were walking by. Suddenly I saw a girl put her hand on her chest and fall down, and blood was coming out of her mouth and nose," the alleged driver said, according to Press TV.
The report claimed that the driver's comments serve only to add to the "confusion already surrounding the shooting, which has been blamed upon Iranian security forces by the Western media hype."
Press TV claimed the first indication that her death was suspicious was the discovery that she was killed by a small caliber handgun, "a weapon that is not used by Iranian security forces."
"Policemen are not authorized to use weapons against people," Tehran Police Chief Azizallah Rajabzadeh said, according to the Press TV report.