Nassau police are investigating whether Friday's shooting of a 12-year-old Hempstead Village girl when a bullet flew into her living room was gang-related retaliation gone bad, a law enforcement source said Saturday.

Police are offering a $75,000 reward for information in the hunt for the shooter.

Dejah Joyner remained in "grave condition" Saturday at Winthrop-University Hospital in Mineola after being shot in the head in her living room on Dartmouth Street, Nassau County acting Police Commissioner Thomas Krumpter said. The bullet entered her brain, he said.

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Krumpter vowed to catch the shooter responsible for "this heinous criminal act . . . committed by a despicable human being."

"My heart is broken," Hempstead Village Mayor Wayne Hall said on Saturday. "I'm asking . . . whoever's done this to come forward and give yourself up. We're not going to stop until we find who shot this young lady."

Police said the investigation is being led by homicide detectives with the help of the special investigations squad dedicated to gangs, the criminal intelligence unit and others.

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The law enforcement source, who has knowledge of the investigation, said detectives are looking into whether Friday's shooting was a gang-feud-related, retaliatory drive-by shooting gone amiss -- a shot that missed its intended target.

Police swarmed the Hempstead neighborhood as detectives combed the front yards of adjoining Dartmouth Street houses and the front yard of the victim's home for clues.

Police said a shot was fired from outside, and the bullet pierced a front window, hitting Dejah in the head as she stood in the living room.

Dartmouth Street neighbor Lorena Reyes, 32, said she was cooking in the kitchen when she heard the shot. She and 12-year-old daughter Lorena Martinez, a close friend of Dejah's, looked out the window and saw the girl's parents emerge from the house, screaming, " 'Oh, my baby!' " and " 'Dejah!' " Reyes said.

About 10 minutes later, Lorena Martinez saw paramedics take her friend out of the house in a stretcher. Dejah lay motionless, she said, and blood covered the right side of her head.

Witnesses said they saw what looked like an older-model dark green or black Nissan speeding away in the moments after the shooting.

Krumpter promised ramped-up patrols as the investigation continues.

"There will be a visible, significant increase of both Nassau County police personnel and Village of Hempstead police personnel as we move forward," Krumpter said.

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Krumpter said the ShotSpotter system covers the area where the shooting happened and that investigators are looking to see what evidence it picked up. The village recently added security cameras to its ShotSpotter system and replaced all of its streetlights with LED lights to show more natural light and deter crime.

Acting Nassau District Attorney Madeline Singas promised justice for Dejah Joyner.

"We need to stop gun violence in our community. We cannot sit idly by as 12-year-old children are gunned down in their own living rooms," Singas said Saturday. "This person . . . will pay for what he did to that 12-year-old."

Residents stopped outside the house Saturday to say a prayer for Dejah, and lament the violent history of their neighborhood.

"We've been through this too many times," said Naisha Mason, 24, who lives two blocks away. "It takes a child getting shot to wake people up to what's happening."

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Hempstead school board president Lamont Johnson said counselors and psychologists would be available for students Monday at Alverta B. Gray Schultz Middle School, where Dejah is a seventh-grader.

He said he knows Dejah's father and grandfather, who he said were heartbroken and in disbelief.

"The father was very upset. What happened to his daughter is a tragedy and words can't explain how he feels," Johnson said. "Everyone feels like a 12-year-old child in their own home should feel safe, and there's too much violence. Everyone says enough is enough of this senseless violence."