>>Dafter and dafter :-}
>>Why didn't the driver sue the owner of the bird for allowing it to stray onto a public highway and damaging his car?
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>I think you can do that for a dog, horse, ..
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>But not for a cat or a bird

I know that here farmers are liable for livestock straying onto fenced roads. And livestock includes poultry and poultry includes geese.
An important bit of that is fenced roads - if they are unfenced then the onus is on the motorist. No idea what applies in the U.S. though.

I think you're right about cats and dogs. Interestingly, if you run over a dog in the UK you have to report it to the police ; if you run over a cat you don't.....