One clear-cut benefit to working with a shelter or rescue is that they may know a pet's history and may be able to tell you if they've lived with another pet of a different species.
"Choosing a dog who's lived with a cat and vice versa is usually a good way to go," said CJ Bentley, Behaviorist at the Michigan Humane Society.
And if you have an adult cat, it's best to match her with a similarly aged pet of the other species, since an energetic puppy may likely set an aged cat on edge.
The First Meet & Greet
Take precautions: make sure the dog is leashed when first meeting the cat. While the introductory meeting may seem to be going smoothly, it all can change in a flash if the cat makes a run for it. So it's best to make sure the cat has a clear route to escape, and the dog is restrained should his predatory/chase instincts kick in.
Never Forget What's in a Pet's Nature:
Cats can injure dogs by scratching if they feel threatened. And cats can injure themselves while trying to flee.
Dogs may simply be too big or rambunctious for a cat to handle. And an unintended invitation to play can lead to injury.
"Remember too that just because an animal 'tolerates' a new family member, it doesn't mean they really enjoy the other's company," says Bentley. "And some dogs just can't relate to cats as housemates.
Best Left Alone
Until you're certain that the cat and dog have accepted each other, it's best to keep the two separated when left alone.