The sky can turn green during severe weather, but a green sky has not been shown to have any specific correlation to tornadoes. The sky may appear to be green before or during a thunderstorm, which shares similar formation conditions with tornadoes.
Researchers at Pennsylvania State University have found that green skies can occur before or during any type of severe weather. The researchers observed green skies prior to thunderstorms and hailstorms but not prior to any tornadoes. It is still unclear as to why skies appear to be green during severe weather, although the moisture in the air may play a role.