Wow, the amount of mis-information in this thread is shocking. For example, LEO are entitled to qualified immunity unless one can prove he was acting outside the course and scope of his employment when the incident occurred. Thus, if a LEO is shooting to defend himself in a gun battle and hits a bystander I can almost assure you he will be entitled to qualified immunity. Whereas when the cops are beating someone the whole point of that is to prove he is outside the course and scope and thus not immune and subject to civil and criminal liability. These are not protections offered to non-government employees. Same can be said when a LEO kills someone in his cruiser.
I'm not gonna bother correcting the rest. But if you want insurance coverage for your own negligence investigate an umbrella policy. It may be of some use.