Lots of studies. Permethrin is safe for most animals, but don't spray it anywhere near cats.
Dogs are OK. You can even spray it on their fur. Dogs can be very susceptible to Lyme Disease. So treat their fur before hiking with them.
It can be harmful to fish and amphibians as well, if I remember correctly. So be careful where you dispose of it.
Wash your clothes after treatment and the permethrin will still work for several washings. I belive that cats don't have issue with clothes after they have been treated and washed once.
A little off subject,
Lyme disease is very common in the North East and becoming more common in other areas, far more common than people want to believe.
I have experienced advanced Lyme and I never want to go through that again.
I know at least ten people who contacted it, but realized it early on and treatment took care of it.
I have a friend who has partial paralysis. We don't know yet if it is going to be permenant.
One friend was hospitalized with brain/nerve problems caused by it and probably won't fully recover.
Permethrin is the best way to avoid Lyme Disease.