We tried to adopt a cat once from a local shelter. If there was any indication that you would let the cat outside, for any period of time, they would reject the application. Also, if there was any indication you would ever leave the cat alone for 10 hours or more, they would reject the application. So, we left all those cats in the shelter, where there were almost certainly terminated, and bought a kitten from some random people on craigslist.

After that cat passed, we tried to adopt a dog from the local shelters. All required an interview and house visit, with random unscheduled visits within the 6 months after. We bought a puppy from some random kid.

edit: "any indication that you would let the cat outside" and "outdoor cat" are not the same thing. I failed because I said we had a patio we would let the cat sit on, in nice weather, on the second floor, or because we were going to see if we could leash train it (my friend had with his cat). I don't know, the lady seemed very angry the whole interview. The leash training failed before it made its way outdoors, but the sun was enjoyed.