Great question!

First of all, the number of people who died as a result of or in connection to the riots is still disputed. The Los Angeles Times says as many as 63 people died, the New York Times uses your number of 58 people, and still another source suggests that 53 people were killed. Overall, I think it’s reasonable to say that around 60 people died because of the riots.

Regardless of the exact number, a significant majority of these were homicides. In the article I linked to above, the New York Times says 50 of those deaths were considered homicides; this is fairly consistent with other sources I’ve read. Not all of those who died were murdered, however. The last article I linked to above suggests that at least 6 people died in car accidents that weren’t hit-and-runs, while another 6 died as a result of arson.

However, I still haven’t answered your question. That’s because the Los Angeles Times has a site that gives you much more data about the deaths caused by the riots, including a map showing where each of them occurred. To summarize it, however, 10 people were killed by law enforcement officials while 44 others were killed in “homicides or other incidents tied to the rioting”. Even if some of those 44 others were not the result of homicides but instead “other incidents”, that still means a distinct majority of the deaths that occurred during the riots were the result of civilians and not police officers or national guardsmen. I hope this answers your question!

–

Ninja edit

A footnote on the last article I linked to says that there were 36 riot-related homicides. In other words, of the 44 killed in “homicides or other incidents tied to the rioting”, 8 were not homicide victims and 36 were. However, the note goes on to say that “of the 36 riot-related homicides, 23 remain unsolved.” A final answer to your question—10 individuals were killed by police officers, 36 by others. We may never know exactly who was responsible for many of these murders.

In the context of how you are asking, I believe you would categorize the majority of specific deaths directly caused by others as "civilian vs. civilian". Of course there were instances of police using lethal force, but in the wholeness of the riots many individuals used the moment to impede upon their enemies or carry out acts of violence knowing that their actions may not hold repercussion purely due to the chaos at the time. For example, the Reginald Denny video somewhat illustrates the point I am making. There is a degree of violence that can be seen throughout the riots that is simply reflective of a populace who then believed that there was too much chaos for law enforcement to handle. And also this includes essentially setting someone else's home/business on fire whether they were aware that people were inside or not (There is a PBS Frontline from the mid 1990's that highlights this very well by the way).

Finally it is important to note that the National Guard did not arrive until Saturday, essentially the 4th day of the rioting. And by the time the National Guard arrived and was furthermore reinforced by the Marines from Pendleton, a majority of the rioting had died down. Although there were one or two minor altercations between guardsmen and civilians (a driver attempted to run his car into a National Guard barricade and was killed), the bulk of the violence during the riots was between the civilian populace themselves.