A sister site has a post Is Permethrin safe for cats after it dries? it has a well referenced answer saying that cats should be kept away from Permethrin before it dries.
But there have been some answers and comments suggesting that some veterinary professionals believe Permethrin can harm cats even after it dries.
Is there any research showing dangers to cats from dried Permethrin?
There appears to be some claims that Permethrin is very toxic to cats. The Wikipedia article for it links to a few sources. A general fact sheet stated:
Cats that have been exposed by accident to products with high (45-65%) levels of permethrin may seem anxious and can't walk normally. They may also have muscle tremors and seizures and they may die from the exposure.
Another source claims:
...the pesticide permethrin, a common ingredient in some tick-prevention products for dogs, is highly toxic to cats. If you have a dog and a cat, and the cat regularly licks or grooms the dog, avoid using permethrin on your dog
A third source was cited on the Wikipedia for the substance as well.
While these sources seem to be more about direct usage on cats, I feel that it's within ones best interest to avoid using this substance at all if you have cats. It seems what happens most often is people who have both cats and dogs apply some of this to their dog(s) and eventually some of it could get on their cats from just "getting around" for a lack of a better term. Although you asked if dried permethrin could pose a threat, I would still avoid using it or products that contain it if you have cats.
Edit:
As I said, the above is more about direct contact with fresh Permethrin. In doing some additional searching, I've found the following article:
If you are spraying a 1 percent concentration on clothing and it dries, it's unlikely that you'll see any problems with the cat
This article discussed both usage on dogs and usage for humans, mainly with regards to spraying it on clothing. It seems most sprays that humans would typically use are far lower in concentration than that of what you would apply to your dog. Because of this, the risk to cats is far lower. They still recommend spraying clothing with the substance away from your cats and in an area where the cats cannot access, and to be sure it is fully dried before coming in contact with your cats again.
My conclusion is then if you are using this with your dog(s), the concentration amount of Permethrin is typically far higher, thus it poses a more severe risk to cats. As said before, it is possible the cats may come in contact with it by accident if you are using it on your dog(s) and thus it could cause harm. In regards to the type of products humans use for clothing, it's far less likely to cause any issues especially if you let it dry since the concentration of Permethrin is usually much lower. But if you want to be absolutely safe and eliminate all risk, then it is best to avoid it then.
