According to Pearland police, 38-year-old Geoffrey Ferguson told a friend he was responsible for the killing.
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The shooting happened on Sunday just before 5 a.m. in the 1600 block of Rayburn Lane.
Officers responded to the home and saw Ferguson inside a bedroom and took him into custody, police said.
They found the body of his 69-year-old father, William Ferguson, in another bedroom with multiple gunshot wounds.
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It's still unclear what led to the shooting, but there were no other suspects or victims involved in the incident, police said.
Geoffrey Ferguson called a friend and told them about the killing, according to investigators, and that person was the one who called 911.
The incident remains under investigation.