But that's the problem! The civilian shouldn't be going to jail, either, should they?
That is, I don't think the standard for prosecution for killing someone should be different for civilians and police.
Some would fix the problem by giving the police special immunity; I'd fix it by changing self defence laws for everyone.
Or perhaps, to put it another way, under what situation could you imagine yourself as a juror convicting a civilian of murder, but acquitting a police officer who acted identically?