Chicago police say the shooting happened in the city's South Shore neighborhood.
The owner of the home, a woman in her 70s, is being questioned by police. So is the 12-year-old boy.
The incident happened near 76th St. and Coles Ave.
Neighbors said months of harassment, profanity and disrespect led to the shooting.
"His name? As far as I know him, I call him the little bad boy," said the suspected shooter's neighbor, Hilda Brunt.
On Tuesday night, there was surprise, but little sympathy from some, for a 12-year-old boy shot in the arm.
Police say a woman in her 70s suspected the boy broke her window. She went inside, got a gun, and fired several shots. The woman's neighbors say this particular boy is no stranger to them.
"He broke her window. He set her grill on fire. He started a fire last year across the street - the rowhouses. I had to call the fire department," said Hilda Brunt. "I know it's the same boy."
Frenchie Johnson, also a neighbor of the suspected shooter, said she had to have sympathy her neighbor.
"She talked to me on Friday she said, 'Frenchie I've done had enough.' They set the garbage can on fire, her barbecue pit, this isn't the first time they busted a window. It's bad," said Johnson.
"I saw the kids earlier," said South Shore resident Jennifer Ramirez. "They were outside throwing bricks, and I told them I was gonna call the police if they didn't leave, so they walked off, and about an hour later, I heard three shots."
The 12-year-old boy's family paints a different picture, claiming the window was already broken by the time the boy and his friends walked by.
"I hope they took her to jail, I hope so, something's wrong with her," said the boy's grandmother, Donna Virges. "My blood pressure has gone sky high thinking about what could have happened to him."
Detectives questioned both the boy and the woman Tuesday night.
The 12-year-old's family said Tuesday night that they have heard that police are thinking of charging both the boy and the woman, a sign that police may think both bear some responsibility for the incident.