I know that the targeting of officers was not permitted in European armies. American military leaders were mostly veterans of Britain's war against the French and Natives, so they knew how European armies fought. America modeled its military after the British, French, and Spanish; dressing ranks, firing vollies, and for the most part, they didn't shoot officers specifically from what I've seen.
The veterans that fought for the British and didn't become officers joined militias. They knew the capabilities of the British and they knew that the British war methods could work against them if they didn't fight the same as them.
The Militia fired from cover, fired as often as they possibly could, and in some historical cases, fired upon officers first to plunge the larger British force in disarray.
I pretty sure the Continental Army didn't intentionally kill officers. Yes they may have killed a few due to stray bullets, cannon fire, ambush, ECT. However, I'm sure the Militia targeted the officers first so that no matter how small their force was, they could beat the unlead, highly disciplined soldiers.
But this is not 100% accurate. I could be wrong. I could be VERY wrong. So don't take what I have written as fact, but at least consider it.