After shooting dead an unarmed teenager in his bathroom, a New York City police officer threatened to kill the boy's distraught grandmother, a newly filed lawsuit alleges.

Filed Friday, a day before the one-year anniversary of the death of 18-year-old Ramarley Graham, the suit accuses the NYPD of improperly training its officers, disproportionately targeting minority youth through its controversial stop and frisk practices and covering up the facts surrounding the death.

The suit names police officer Richard Haste, the man responsible for shooting Graham, as well as NYPD commissioner Ray Kelly and a number of other officers as defendants.

Haste was charged with first and second degree manslaughter in June. He is the first serving NYPD officer to face criminal charges for a fatal shooting since 2006. The four-year veteran of the force faces a maximum of sentence of 25 years in prison if convicted. He has pleaded not guilty.

On Saturday, to mark the anniversary of Graham's death, his parents and hundreds of supporters marched from the home where he died to the precinct where the officer who shot him was assigned.

As the crowd approached the building, Franclot Graham, Ramarley's father, turned to a man organizing the march and said: "Tell them we're going to tighten up and tell them we're going to get loud."

About a dozen NYPD community affairs officers and interlocking metal barricades separated the chanting demonstrators from the 47th precinct. "Last year, February 2, it was our son," Graham told the officers by megaphone. "Next year, who's next?"

At over 100 pages in length, the Graham family lawsuit paints a picture of a chaotic scene the afternoon Ramarley was killed. It alleges that after forcing his way into the Graham home, Haste shot the unarmed teenager in the chest in his bathroom, as his six-year-old brother and 58-year-old grandmother, Patricia Hartley, looked on.

"Why did you shoot him, why you killed him?" Hartley cried out after Haste fired, the suit claims. "Get the fuck away before I have to shoot you, too," Haste is said to have replied as he shoved Graham's 85-pound grandmother into a vase, the suit alleges.

According to the suit, NYPD officers twisted Hartley's arm before taking her into custody for nearly seven hours where she was questioned, accused of covering up for her grandson and denied access to her attorney for over an hour and a half.

"They were calling her a 'fucking liar'," Jeffrey Emdin, an attorney for the family told the Guardian. Emdin believes the grandmother was isolated to intimidate her. "It's my assumption that they were trying to rattle Ms Hartley into saying that her story couldn't be true," he said.

At one point during Hartley's questioning, a police officer allegedly dunked his fingers into a glass of water then splashed the liquid against a wall. "They were demonstrating how blood splatters after someone is shot," Emdin said.

According to the lawsuit, the police also showed Hartley a photo of a man who had been shot and claimed it was Graham. Once released, Hartley was "totally exhausted, totally traumatized", Emdin said, adding that she sought treatment for trauma in a hospital.

The NYPD searched the Grahams' home for 48 hours following the shooting and the family was unable to return, the suit adds. The suit, which does not specify damages, calls for an overhaul of training practices for street narcotics enforcement units, otherwise known as SNEU. Haste was a member of one such unit, which scans streets for suspected illegal drug activity, but had not participated in the required training for the assignment, reports later revealed.

Graham's brother and sister, Chinnor Campbell and Leona Virgo march with supporters to a nearby police precinct. Photograph: Ryan Devereaux for the Guardian

When news of Graham's death broke, the police initially said he had disobeyed orders to stop and ran into his home. Surveillance footage later showed him calmly entering his building. Moments later officers are seen rushing to the door, attempting to break it down.

Haste chased Graham into his second floor bathroom where the shooting occurred, believing he was carrying a gun. A small bag of marijuana was found in the toilet near Graham's body but no weapon was ever recovered.

After the incident, Haste and his supervisor, sergeant Scott Morris, were stripped of their badges and guns. A grand jury was convened and district attorney Robert Johnson's office joined the NYPD's internal affairs bureau in a four-month investigation.

Haste's attorney, Stuart London, has argued that his client had no choice but to shoot Graham after he failed to show the officer his hands. According to London, three members of Haste's team have stated they saw a gun on Graham in the moments that led up to his killing.

The NYPD did not respond to a request for comment. The next court hearing in the case is scheduled for 26 March.

In the wake of Graham's death, Kelly ordered a review of the narcotics enforcement units, which were credited with reducing heroin and crack dealing on the streets of New York in the 1990s and more recently have concentrated on marijuana. This has been a source of controversy, with officers accused of forcing suspects to reveal small amounts of marijuana in their pockets, despite a ruling by Kelly that police should not make arrests for the possession of small amounts of cannabis in private.

Graham's family hopes that the legacy of his death is an overhaul of police practices. In the freezing cold on Saturday, Graham's mother, Constance Malcolm, addressed the crowd of supporters. "We want people to remember what happened to Ramarley and hope another family doesn't feel the pain we're feeling. It's a pain I hope no other parent will have to go through."