In order to determine correctly whether the plant is toxic or not, you will have to get the botanical name of the species you have.
The chief problem that you have with Jasmine is that there are quite a few different, unrelated species of plants that are known by the common name Jasmine (e.g. the Jasmine shrubs of the species
Jasminum, the very common Star Jasmine of the
Trachelospermum species, and the Night-Blooming Jasmine/Jessamine of the
Cestrum species).
The Cestrum species in particular comes up in a lot of plant lists as highly toxic (see
University of California, Davis Toxic Plants List and
Melissa Kaplan's Harmful & Poisonous PLants)
I haven't seen the other species mentioned on any toxic lists, and the UC-Davis site does have Star Jasmine (
Trachelospermum) on it's Safe Plants list (
University of California, Davis Safe Plants List).
So until you can correctly determine the scientific name of the plant you have, and then positively confirm that it is not toxic, I would rather err on the safe side and avoid using the plant.
Also remember that most of these Toxic/Safe lists were determined with regard to humans/mammals, and so may not be accurate for reptiles. There is a school of thought that says that if the plant doesn't come from the animal's native habitat, it may not be safe to use the plant, since the animal's species would only have evolved to avoid toxic plants that are found in the area it comes from.