Officers encountered the man, later identified as Jacobo Cedillo, 50, of Los Angeles, on April 8 around 4:15 a.m. sitting down in the driveway of a Van Nuys gas station.
They spoke to him and, believing him possibly to be under the influence of a drug, placed him in handcuffs.
There was a struggle and the man briefly broke free from the officers. They took him to the ground to control him and at one point, he lost consciousness. Paramedics treated Cedillo at the scene and then transported him to a nearby hospital.
Police say a preliminary test at the hospital indicated the presence of methamphetamine in his system.
Cedillo died at the hospital five days later.
Police say Cedillo had prior arrests for assault with a deadly weapon, exhibiting a deadly weapon and driving under the influence of alcohol or drugs.
The investigation into the incident is continuing. The official cause of death has not yet been released by the county coroner's office.