Christopher Dorner was shot at by a fish and game ranger, as he fled in a stolen vehicle in north-east Los Angeles, Reuters is reporting.
The agency states that earlier Dorner had broken into a home, tied up a couple and stole their pick-up truck.
Local media is also reporting it is believed one of the hostages was able to flee and raise the alarm.
More top news
Support for new parents has faced deep cuts in recent years - and some social workers warn it could lead to a rise in forced adoption.
Theresa May and Donald Trump will meet for talks at the World Economic Forum next week in Davos, in the Swiss Alps, Downing Street has said.
Cameras caught planes having a rough ride coming into land, after days of storms across northern Europe which left nine people dead.