Signal crayfish (American ones) eat their own young so taking adult crayfish makes the population grow rather than decline (god knows how having more of something that tastes yummy is a bad thing
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) so they very rarely give permits to individuals to catch them.
Having said that, if you were to set a trap "to target eels" or something not restricted & you get a couple of crayfish in the trap, it's then illegal to release them back into the wild. The law stated they must be dispatched & disposed of. I have read cooking is a good way to dispatch "unwanted" crayfish & inserting the cooked meat into the stomach of the human species via the mouth is a very good way of disposing of them
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Also a tin of tuna in sunflower oil is supposedly good at attracting crayfish to traps so you better not put one of those in. I read a couple of nail holes in the top & bottom of the tuna tin is a very effective method of releasing the scent trail. Again best not to do this as you don't want to be accused of secretly targeting crays with your eel trap.