Police say the homeowner saw Deyfon Pipkins, 33, trying to climb into the window and fired his weapon at least once at the intruder.
The homeowner is legally protected by the Castle Doctrine, which allows a person to defend his or her home against an intruder.
"It means they don't actually have to retreat once someone comes in their home," Sergeant Calvin Johnson, Dallas Police Department, said. "You have the option of using deadly force if you believe your life is in danger."
After police notified relatives of Pipkins' death, some showed up at the house. They were upset, and questioned the homeowner's actions.
"He could have used a warning," Lakesha Thompson, Pipkins' sister-in-law, said. "He could have let him know that he did have a gun on his property and he would use it in self-defense."