Equivalent idiomatically - yes, but has nothing to do with any animals.
The Polish saying is "Leje jak z cebra".
"lać" here means "to pour down", "to rain intensively". It's a colloquial word, but a common one.
"ceber" used to be a big wooden bucket used to carry water or other liquids. Nowadays this word is almost only used in this saying, and many Polish people may not even know what exactly a 'ceber' is. Or rather was.
So anyway, this is literally 'It pours like from a wooden bucket'.