The gunman, 23-year-old Dejon White, was later killed by other officers when he allegedly grabbed a shotgun.
Family members say White was a quiet man, seemingly untroubled.
"It hurts, it really hurts," said White's mother, Tamica Berason. "I'm so sorry for everybody, for this whole thing happening. If I would have known my son needed help, I would have got my son help."
White was working for Urban Corps, an organization that helps disadvantaged young adults. Officials there said he showed no signs of anger.
After White was killed by police gunfire, officers found a suicide note in his apartment, but it revealed no motive and no clue that he would fatally shoot 36-year-old officer Jeremy Henwood in the head as he sat in his patrol car Saturday afternoon.
Henwood was pronounced dead early Sunday morning. A four year veteran of the force, he was also a member of the U.S. Marine Corps Reserve and recently returned from Afghanistan.
Just before the officer was shot, police say the gunman opened fire on a man who was sitting in his car at a fast food restaurant. He was wounded in the face, but is recovering in a hospital.