They will take any animal you bring as long as it was found in their jurisdiction.
As far as I know they do because one of the staff members picked up a bird from the floor that had a broken wing when I used to volunteer here. But to make sure I am giving you the appropriate answer I strongly suggest that you go directly to this facility tomorrow and speak to an officer or to an animal care technician at the front counter. As I am sure you probably already know they open from Monday through Saturday from 8:00 a.m. to 5:00 p.m. and on Sunday from 11:00 a.m. to 5:00 p.m. It might also help if you call the city's number at 311 and ask to be transferred here. Good luck!
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