Doug, it varies by the state, how they are handled. Most often, the officer will offer the deer to whoever hit it, if they want it. The officer may need to write out a tag for claiming that deer.
Here, in Ohio, a hunter with a valid deer tag, must use that paid for tag to claim it, (something many disagree with. No one else is required to spend money to claim it, and it may be your only buck for the year)
Sheriff's departments, often have sign up lists for roadkill, and you may be called day or night to show up and. Claim the meat. You might only get half of a deer as usable meat. But it would be a fresh killed deer, and free. Not a bad deal, as long as you have a place to process it cleanly and quickly.
The only real difference between a good tracker and a bad tracker is observation. All the same data is present for both. The rest is understanding what you are seeing.