The OP said permethrin, not pyrethrum. Of course permethrin (especially when encountered as a liquid), like any pesticide, can be carcinogenic, which is why it's extremely important to take precautions (like rubber gloves and a face mask, and applying it outdoors) when using it. It's also a broad-spectrum pesticide which can kill a number of beneficial insects, so its use should be limited.

I have been known to spray my tent door netting when going into a really buggy area, which hopefully keeps an accumulation of hungry bugs from zooming in before I can get out and close the zipper. As the other responders have mentioned, there's no point in spraying the tent itself. IMHO, the less chemicals used, the better.