You'll probably have to wait and watch for a while to see if it's tree or herbaceous coming up. Tree peonies do put up new growth from the ground as well as from the woody limbs. Do you know how old the tree was when you got it? Did you see the roots? Tree peony roots look different from herbaceous. If you didn't see traditional skinny yam looking feeder roots when you dug it up then your tree has developed its own root system and you won't have to worry about it at all. The tree peony roots look more like any other shrub, one of the forum members referred to them as looking like a bird's nest! There's a really good picture of what he was talking about on the GardenWeb peony forum, or maybe he'll post on this one, too, since he's on both.
If you're not sure whether your new growth is tree or herbaceous when it leafs out a bit more post more pictures; we'll look and try to help if possible.
