I can't answer for everywhere but I can answer for my town and my incident.
- PD policy is if you draw the gun you have to fill out a long report. Officers don't like writing reports! Don't know for certain, but I would suspect that any officer who fires their gun (for any reason) will go thru an "inquisition" by the chief! [In my 17 years as a Special PO, I drew my gun only twice due to circumstances but neither case was it drawn against a person. I never filed any reports, but our chief then was 100% RKBA and he wouldn't have hassled us. Current chief is a whole 'nother story.]
- Our chief is 100% anti-gun, hates them and has cursed that he has to carry one when on duty. He even initially refused to issue any new LTCs when he came into town. [Important, see later.]
- When we hit the deer (er . . . it hit us), the deer did a somersault and landed sitting on its legs (looked like a postcard picture) at the edge of a driveway on a relatively busy street. The family who lived there came out, Mother, Father and kid to see what happened. People in house across the street stepped out on front steps. The deer just stared into my headlights (I wanted to blind it to prevent it from trying to get up and wander) and the pose was such that many would guess that the deer wasn't really hurt. A couple of times it attempted to stand but couldn't get off the ground (broken legs no doubt).
- If anyone had shot the deer at this point, the phone calls and letters to the editor would have flown about how someone recklessly shot an innocent deer that "wasn't hurt" (live in a classic "tree hugger town"). With families standing around it would be real ugly to do that with spectators. [My Wife actually wanted me to call a vet for the animal, so she would probably never have forgiven me if I had shot it.]
- I am no longer a police officer, and although I was CCW'g a 9mm, I would only have used it if the deer got up and started wandering around in traffic (a clear and present danger). Also, not being a hunter, I would not have known positively where to place a bullet for a one-shot, instant kill without chance of ricochet (hitting skull bone?).
- If I had drawn my gun, the chief would have had my head and probably my LTC as well!. He just loves to find excuses to revoke LTCs.