Is anyone aware if Composite Crossbows, those used in europe roughly in the 12th-16th centuries were in any way built in a recurve fashion?

I.E. the bow does not bend back to straight but past straight?

I don't know about European crossbows, but many Chinese crossbows had prods that were definitely built in a recurved fashion--especially if we accept the theory that at least some Chinese crossbow designs were basically just ordinary hand bows lashed onto the end of a tiller.