According to a study by Newsweek magazine, only 2% of civilian shootings involve an innocent person being shot (not killed). The error rate for police is 11%. What this means is that you are more than 5 times more likely to be accidentally shot by a policeman than by an armed citizen. But, when you consider that citizens shoot and kill at least twice as many criminals as do police every year, it means that, per capita, you are more than 11 times more likely to be accidentally shot by a policeman than by an armed citizen. That is as low as I can get that number. This is not meant to be an indictment of the police. In fact, because police often live on the edge, they naturally tend to shoot first and ask questions later. Although they are trained to repress this instinct, it does not always work, as evidenced by the number of innocent people killed by police. Also, since they are generally better marksmen, they tend to kill, rather than wound or totally miss their target.
The Kleck study shows that police shoot and kill around 600 criminals each year. Yet the University of Chicago study shows that police killed 330 innocent individuals in 1993. That means that for every two criminals killed by police, one innocent citizen is killed by police. Although I have the greatest respect for the police and how they must respond under pressure, I think that I would much rather trust an armed populace.