At about 4:55 p.m., the officer was trying to wake up a homeless person near Alvord Lake on the eastern side of the park near Stanyan Street when the transient's dog started barking, police spokesman Officer Albie Esparza said.
The officer backed away, but the dog, believed to be a pit bull mix, broke free, ran toward the officer and bit him, prompting the officer to shoot and kill the animal, Esparza said.
No other information about the case was immediately available.
