Cuckoo means crazy as it is an allusion to the cuckoo birds eponymous and monotonous call.
Cuckoo birds are said to be crazy as they are brood parasites and manipulates and relies on other birds to raise their young.
The common cuckoo bird does not make a nest of it's own and instead the mother cuckoo uses another birds nest to lay their eggs in and the other bird takes care of the cuckoo babies.
The earliest known use of the noun cuckoo is in the Middle English period (1150—1500). OED's earliest evidence for cuckoo is from around 1240, in Cuckoo Song.
The word cuckoo is of multiple origins.
Either (i) an imitative or expressive formation.