Is it safe to put a frozen dead mouse that has been thawed out into an alligator snapping turtle tank levels have never been checked?

It is most likely safe to add a frozen dead mouse that has been thawed out to a alligator snapping turtle tank. If the tank levels have never been checked the addition of a corpse could add ammonia to the tank which would not be favorable to the turtle and could lead to premature death. Alligator snapping turtles can eat mice, and if it was store bought it will be fine to feed as long as it hasn't been sitting out for any more than a few hours.