There was recently a large, front page, article in our local paper about the secondary effects of rat poison. Yes it can kill your chickens and other animals who consume a dead or dying rodent. It usually takes a rodent 4 -5 days to die and as it gets sicker and more careless there is greater chance of it being found and eaten by something. At some point they hemorrage to the point of dropping dead, maybe in their burrow, maybe anyplace at all, so it's common to find them lying around. Even after it is dead it is a danger to other animals until the body has decomposed.
The active ingredient in the worst ones is Brodifacoum, Bromadiolone, or Difethialone. Commonly known as D-Con, Just One Bite and others.
I was using the Just One Bite because we had a mouse population explosion here this spring, in spite of keeping feed put away etc. etc. Went thru quite a bit of it too so I'm sure we knocked down the population quite a bit. But this last week I'd found a few dead mice and a dead rat near the chicken pens and after reading that article I was concerned for my chickens, cats, and dogs. Not to mention owls and whatever else may find those poisoned critters. Nasty stuff. So now I'm going back to plain ole' traps I guess.