The cat in the most recent incident survived and is now looking for a good home, but authorities say it is not the first time that a cat was dumped inside a bucket.
Police say the man left the sealed bucket that contained the cat near a garbage can in front of Animal Haven on Thursday.
The man then fled on foot.
A worker leaving for the night saw the bucket and heard a hiss. The bucket's lid had a hole in it, and officials said the cat was malnourished.
A similar incident happened a month ago, when another worker found a plastic bucket near the trash outside the shelter's back door.
Peeking out of the hole on top was a cat, which was brought inside, checked out and named Sage.
The suspect is described as an Asian male who was last seen wearing a sweater, jeans and dark-colored shoes.
Anyone with information in regard to this incident is asked to call the NYPD's Crime Stoppers Hotline at 1-800-577-TIPS (8477) or for Spanish, 1-888-57-PISTA (74782).