Mohammad Usman Chaudhry was shot after Officer Joseph Cruz and his partner found him lying by bushes behind a Hollywood apartment building in March 2008.
A police probe largely cleared Cruz after he said he shot Chaudhry when the 21-year-old man lunged at him with a knife.
But Chaudhry's family said he was not violent and claimed Cruz had planted the knife.
Family attorney Olu Orange said a seven-member jury determined Cruz had used excessive force and his conduct was reckless, oppressive or malicious.
City attorney spokesman John Franklin said it was too soon to comment on the findings.
"We are not going say anything at this point until we have had a chance to review all the documentation in the case," Franklin said.
Court documents indicate Cruz was later fired from the Police Department in an unrelated matter for letting a prisoner escape then lying about what happened.
Jurors were scheduled to weigh damages in the Chaudhry case on Tuesday.
The case highlights the growing issue of how police deal with people with autism and other developmental disorders.