i suppose if you wanted to you could try to boil the branches before giving them to your rats, it would kill off anything living in the wood, etc. seems a lot of work though, and i don't think, unless the tree is visibly not doing well (has spotty leaves, etc) that you'd have to worry too much.
i just know that fish hobbyists boil branches before putting them in tanks, but that's because fish are super sensitive to anything in water, and you don't want them getting sick and dying. your rats probably won't *eat* the branches, just chew on them, so i don't think you'd have to prep them.