Hi Stephanie,
I am not sure exactly what you have. If it does not list a chemical as the active ingredient, it is probably a natural extract of chrysanthemums. The natural chemicals in that extract is the model that was used to design the synthetic pyrethroid insecticides. Both the natural and synthetic pyrethroids are relatively safe insecticides. They are highly toxic to insects, but human and animal toxicity is low-- also they are not persistent and will decay naturally.
If there is a chemical listed, give me the name and I can get the toxicity data.
Skeet