No. They do euthanize some. Their website explains it.
When a shelter uses the words "animal control", it is usually because they are controlling the animal population by euthanasia after the animals are up for adoption for a certain period of time. Typically, Humane Societies will be no-kill shelters, though, for the word "humane" is in their name. Other than that, there are other privately run rescues that are also no-kill shelters. It's always best to simply call them up and ask if they are if it isn't clear on their website.
Yes. Call to verify
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