The growth habit, leaf shape and the way they hang from the branches tells me that it is 'Ukigumo'. The trouble is finding one that is white like that one. Someone who has visited Kubota Garden, Seattle WA may be able to verify that it is 'Ukigumo' for sure.
I'd try this contact information to see if you can end up talking to one of the Kubota gardeners. http://www.seattle.gov/parks/park_detail.asp?ID=415
Good point Ron. I see they also have a Facebook page too with contact info. https://www.facebook.com/pages/Kubota-Garden/144013716362 Maybe next time they prune it you can take some under stock and get some grafts of it.
