On Monday, Antonio LeGrier filed a wrongful death lawsuit in Cook County Circuit Court, alleging the officer shot his son without justification, used excessive force and failed to provide medical care as he lay bleeding on the floor.
Antonio LeGrier also sued on grounds of false arrest. He is seeking damages exceeding $100,000.
City officials did not immediately reply to CNN's request for comment on the lawsuit.
Police said officers went to the LeGrier residence early Saturday morning after Quintonio LeGrier, 19, threatened his father with an aluminum bat.
Antonio LeGrier called police and then called his downstairs neighbor, Bettie Jones, to open the door when officers arrived, CNN affiliate WLS reported.
LeGrier charged down the stairs carrying the bat, WLS said. Police opened fire, and both LeGrier and Jones were fatally shot.
Jones, a mother of five, shouldn't have been shot, police say. She was "accidentally struck and tragically killed" by an officer.
Emanuel cuts short Cuba vacation
Also on Monday, Chicago Mayor Rahm Emanuel's office announced the mayor would cut short a vacation in Cuba and come back to Chicago on Tuesday afternoon.
"He is cutting his family trip short so that he can continue the ongoing work of restoring accountability and trust in the Chicago Police Department," Stephen Spector said in an email.
On Sunday night, Emanuel ordered changes in how city police officers are trained to handle calls involving people who may have mental health problems. LeGrier's family said he suffered from mental illness, CNN affiliate WLS
"There are serious questions about yesterday's shootings that must be answered in full by the Independent Police Review Authority's investigation," Emanuel said.
Emanuel, under fire for a series of fatal police shootings, directed the Chicago Police Department and the leaders of the Independent Police Review Authority to meet immediately to "determine the deficiencies in the current training, and determine what steps can be taken immediately to address them."
'There's a crisis in this city'
The Rev. Marshall Hatch, the pastor at New Mount Pilgrim Missionary Baptist Church, where Jones worshipped, told CNN on Monday that he suggested to the mayor there be "total and complete transparency" if Emanuel has hope of persuading some Chicagoans to trust police.
"Some of us may be interested in calling for his resignation if we thought he would," Hatch said. "I think he should come back to Chicago. There's a crisis in the city. ... I suggest that he gets back here."
Emanuel was already under pressure because of the shooting of Laquan McDonald.
McDonald, in foster care for most of his life
, was gunned down in October 2014 by Chicago police officer Jason Van Dyke. Video footage showed the 17-year-old walking down the middle of a street then veering away from squad cars, his back to them, when he was shot 16 times.
A freelance journalist sued to have the video released. More than a year later, in November 2015, the video became public and spurred massive protests during the Thanksgiving holiday, many demonstrators then calling for Emanuel to leave office.
Amid that uproar, Emanuel fired Police Superintendent Garry McCarthy
Van Dyke, who has a history of complaints against him
, mostly for excessive force, was charged with murder. He has pleaded not guilty and is out of jail on bond.
Mother: Son was shot seven times
The shootings come as police in Chicago and across the nation are being scrutinized for the use of deadly force.
Family members and supporters of LeGrier and Jones are blaming bad leadership and a police culture of "shoot first and ask questions later" for the deaths. Specifically, they asked why police didn't use nonlethal force, such as stun guns.
LeGrier's mother, Janet Cooksey, said Sunday that police shot her son seven times, once in the buttocks. That meant he was turning away, she said.
"This needs to stop," Cooksey said, tears streaming down her face as she addressed reporters.. "No mother should have to bury her child, especially under these circumstances. The police are supposed to serve and protect us."
The Cook County medical examiner told CNN on Sunday that Jones died of a gunshot wound to the chest and LeGrier died of multiple gunshot wounds. Both deaths were ruled homicides, the medical examiner said.
Other details, such as how many shots were fired, were not released by authorities. It's not known if any video of the shootings exists.
The officer will be on administrative duty for 30 days while the Independent Police Review Authority investigates, Chicago police said. He has not been identified by the police or the wrongful death lawsuit.
"The department extends its deepest condolences to the victim's family and friends," the Police Department said.
'Where was the Taser?'
Cheryl Dorsey, a retired Los Angeles police sergeant and law enforcement consultant for CNN, also wondered why police didn't use stun guns.
"Where was the Taser?" she said. "Why didn't they deploy a Taser? If they didn't have one on scene, they should have had one with an officer who was responding as backup. What was the urgency? There was no exigent circumstance that the officers could not have waited until a Taser arrived on scene."
Dorsey said an aluminum bat could cause injury but "is not a deadly force."
She said "deadly force should have been used (by police) as a last resort and not a first resort."
The mayor has welcomed a U.S. Justice Department investigation
into whether Chicago police have made a habit of violating the law.
"We will be a better city for it," Emanuel said. "It is in our self-interest, because we need (federal) assistance to make the fundamental and necessary changes."