Honestly, I've not looked into it extensively. Not to plead ignorance, but...
Most studies are for humans. and involve skin contact (as it turns out, we are MUCH more harmful to permethrin than permethrin is to us - enzyme reactions on our skin (and all other mammals, except cats who have much less of the needed enzyme) break it down pretty fast, such that less than 2% of what we contact is absorbed. Then our liver pretty quickly handles the rest. There have been studies of it ingested - again, typically no long term effects even with serious quantities involved. Same with the rat studies. and inhaled. Same/same.
But no equivalent studies for poultry, that I'm aware of.