Despite a call for calm from the family, two demonstrators and six riot police were slightly injured and some property was damaged in clashes after the demonstration.
Wednesday evening's protest was outside City Hall, while the previous two were in the northern Paris district where the death took place.
No arrests were made, although four people were still in detention 10 others have been in court following violence at previous demonstrations.
Family speaks to press
The details of the 56-year-old unemployed man's death are "extremely obscure", one of the family's lawyers, François Ormillien told a press conference on Wednesday.
Four out of five of Shaoyao Liu's children were present when he was killed.
One of his daughters, who used the name Sabine to "ensure calm in the inquiry" according to Ormillien, claimed that the police burst in on a "normal Sunday".
"They began to knock, quicker and quicker," she told journalists. "My father tried to hold back the door [...] I was completely panicked. The door burst open and the shot went off."
Sabine, 26, said the officers did not announce that they were police and that her father was knocked to the floor and did not have time to strike the police officer.
He was carrying scissors because he had been preparing to cook fish, she said.
Police allege scissors attack
According to the police version, her father struck one of the officers in the armpit with the scissors.
"While the aggressor tried to strike the injured officer again, one of the policemen fired a shot in response," the statement says.
Police sources have told the media that the victim was known to police for psychiatric disorders and had been detained in a police psychiatric unit after throwing his television off the balcony of the family's flat.
Police were called on one occasion because he was in the street with an iron bar, according to police - a piece of wood, according to the family's lawyer.
Although a neighbour called the police because of the noise of voices from the apartment, the family insist that he was a loving father and had no record of domestic violence.
Fallout in China
The Chinese media have reported the case, one talking of "the racial prejudice of the French police", and the Chinese government has appealed to France to guarantee its nationals' safety and rights.
The officers involved are not working at the moment but have not been suspended, as Chinese foreign affairs ministry official Lu Kang announced earlier this week.
Paris mayor Anne Hidalgo called for all possible light to be thrown on the affair in a television interview on Wednesday.