Well, I have hit (1) a German shepherd and (2) a cat. In either case I had NO responsibility, in the states I was in (respectively, Texas and Colorado). They were animals at large and in either case avoiding them could have been hazardous.
However, in both cases I stopped as soon as I could and went back to see if there was anything I could do to help the animals/owners.
The dog was okay. The cat was not okay, and I went way out of my way to take the cat and her owner to the emergency vet. The owner, who it turned out had written a bad check for the cat’s spay only days before, then disappeared, and I offered to pay for the cat’s emergency care, but the vet turned my offer down. The vet found the cat a new home, hopefully with a much more responsible owner.
I see that I acted properly under the laws of Oregon regarding such, but there wasn’t this kind of law, at the time, where I was, so it was all at my discretion. I don’t know that I would stop for a squirrel, though. I also don’t know if I would have stopped if I’d been on my way to something that really mattered, like a job I couldn’t be late to.
(1) I was driving on a two-lane highway. I was going a little fast, then up ahead I saw a group of children, one on a horse, and a couple of dogs by the side of the road, so I slowed down, somewhat. The dog in question started chasing my car. He basically ran into my car, fell down, and possibly was stunned. He was limping, but the kids declared that he was okay and said he always chased cars and I should not have slowed down, as he didn’t chase the faster cars. (!!!)
(2) I was driving along a narrow one-way street, one lane, cars parked on both sides. I felt a thump. I did not even see the black cat but I knew I’d hit something. Even if I’d seen the cat, I’m not sure there was anywhere I could have gone to avoid hitting her, and a panic stop was out of the question as there was traffic close on my tail. There was nowhere to park, so I went around the block, found a place, walked up to where I thought I’d hit it, and ran into the owner and another girl cussing out the “hit and run driver.” I pointed out that that was me, and there was nowhere to stop. The three of us managed to coax the cat out from under another parked car, and then I took her to the vet. (Owner had no car.)