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
Protesters force cancellation of controversial 'human zoo' show which has been dubbed racist and offensive.
The Silverton family are celebrating the birth of the first baby girl in a century, breaking a streak of 21 boys over four generations.
The 100 leaders did not agree on concrete proposals, but the meeting has raised hopes for concrete international agreement next December.