A couple of years ago, we found a kitten in really rough shape, and no one could take it. We already had our max pet allotment of two cats, but when we were talking to the apartment manager, they basically said "Didn't your mother-in-law move in a while back? Isn't she ill? Could it be that this kitten is her 'support animal'?" wink wink. Most places are pretty cool about it, within reason. If it's an unusual animal, you might raise some alarms. ADA might be law, but it can also be challenged if it presents an undue hardship on the party petitioning it, such as a landlord.