Since Jasmine tea is basically Green or Oolong tea as a base with Jasmine included to enhance the smell and taste of the tea. For this reason the heatlh benefits would be based primarily with the underlying tea used. For more information see the related questions:

What are the health benefits of Green tea? or What are the health benefits of Oolong tea?

Health benefits of Jasmine tea

It is one of hype that various scented teas acts like aroma therapy. Actually one is wasting their money by buying these sort of hyped tea. Chinese believe these tea keep you slim.There is no scientific evidence for that. Most chinese are slim because of their food habit. They do serve these teas before food in restuarants. Probably the hot water in the tea is more beneficial.