Break a femur, humerus or other bigger bone open and look at the marrow. If it is pure white, almost a chalky white then it was a winter kill or maybe killed by a predator after being significantly weakened by the winter. if there's any red or pinkish to it, that is a sign it was "healthy" when it died, so either a lion, a bullet, a car or something like that likely killed it.
It can be tough to tell, depending on how old it is and the conditions it laid out in during the winter. Winter killed critters generally have zero color to the bone marrow IME. This was an elk mandible, skull and backbone/ribs that I found spring bear hunting last year. It has a faint amount of pink to the marrow. The skull had the antlers sawed off and so was the spine, with all leg bones nowhere to be found so it was obviously a hunter killed elk and I suspect just from the previous fall.