Fig.: nonsensical, unbelievable story

What happened to him is so incredible that he cannot even explain it. It would sound a cock-and-bull story

Quello che gli è successo è talmente incredibile che non lo può nemmeno spiegare: sembrerebbe solo una panzana enorme

The suspected burglar thought the police would believe his cock-and-bull story, which was that he had found all that money in a trash bin in the park

Il sospetto ladro pensava che la polizia avrebbe creduto alla sua storia piuttosto inverosimile, e cioè che aveva trovato tutti quei soldi in un cestino nel parco

Where have you been all night? And don't give me some cock-and-bull story that you ran out of gas and got lost in the middle of nowhere looking for a gas station

ove sei stato tutta notte? E non raccontarmi la balla che hai finito la benzina e poi sei finito, a piedi, a casa del diavolo cercando un distributore

The origin of this expression is still uncertain. One theory traces it back to the Old English phrase “a concocted and bully story”; concocted was commonly shortened to “cock,” and “bully” meant “exaggerated”.
Another theory relates this expression to the French phrase "coq-à-l'âne” (cock to donkey), used to describe a nonsensical or rambling story