Definitely find out what it is. My guess on really young cattle and with what you said about poultry liter is salmonella. I had a run in with that a few years ago. Absolutely devistating. 4 calves is 4000 bucks come spring. In all honesty, it doesnt matter what it costs, even if its a thousand bucks its cheap compared to losing another one.
I checked University of TN website and you do have a state lab. If I read it right its free to in state residents for the necropsy. May be a fee for labs but they look to be 100 bucks at most.
If it dies here, and there isnt an obvious cause (like a dead calf sticking out or a bullet wound, dont laugh, Ive seen both, more than once) I take them to the lab. UK charges a 25.00 disposal fee and I have to load and haul them in. Cheap cheap investment in protecting my larger investment.