Technically, I think that it would be illegal for even a police officer to dispath the deer without explicit approval from a wildlife official, but it happens....and for the exact reason you described.

To be quite frank, this happens constantly. My local newspaper now includes a special section just to report deer accidents. As this becomes more and more of a problem, i would assume that wildlife officials may be assuming a much less stringent policy on this. So, I think we have again ventured into the gray area that I am sure others will soon be arguing does not exist.