States animation

I don't think you can. The Animation tab is inactive when you click on to edit the state.

But if you animate the pic for the hover state for example, ahead of time. And then add it as a GIF, as soon as you hover over the pic, the GIF will start playing

The animation options are available to any object you paste into a state while in the edit-states mode. So, for example, you could copy whatever is in the Normal state, delete that item from another state, and then paste the item back into that state. You could then select the item, and give it an entrance animation. That animation would play when you change to that state.

CAVEATS:

• You can't add an exit animation to the original state. That means the original-state object will disappear before the new-state object completes its animation. So this probably won't give you the effect you want with the character. (But it might be acceptable in other cases.)
• Doing this breaks the connection between states. So be careful if you do this with objects that have text, because when you edit the text in the Normal state, that won't affect the text in the revised state. 

As states are just hidden DIVs inside the HTML you can use GSAP for animation on them, I will make a sample.