Can this potentially cause permethrin poisoning?

Hello, I need an advice because I am going to be looking after our family cat. The cat is going to stay with me in a flat that I share with my roomate and her dog. The dog won't be here at the time I will be looking after our cat. The issue is that less then a month ago my roomate used a permethrin shampoo on her dog. After the bath the dog walked basically through the whole flat. I know that permethrin is dangerous for cats, so I want to ask. Is there any chance that the cat can get poisoned from the surfices in the flat?