I know they have dogs, cats, rabbits. I'm not sure about a bird, contact them. there's also Pasadena humane society you can try you can try in case they don't take your baby bird.
Depending on the breed of bird, Pasadena's Humane Society will help. I had a fledgling house finch that I raised and took to them. Burbank had no program for her. They might for other birds. You must be a Burbank resident. Pasadena's didn't require residency. I lived in Burbank at the time.
I don't know for sure but I think that is possible. I suggest you contact them directly
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