Can my pets get mange from a squirrel?

I have seen a squirrel in my back yard every day this week, and the little guy is pretty sad looking. It’s only a guess, but I suspect he has mange.. he is always scratching, and most of his fur is gone.

Can my dogs get mange from being in the yard after the squirrel has been rooting around in the grass? Can it be passed between species? Is there something that I can do to prevent it, if that’s the case?