In a grocery store I came across a EMT she had a sugar glider with her, she said it was a service animal. I was paying for my groceries while we where in line, I asked her what her disabilities were. Can I ask her this question?

Why wouldn't you be able to? It might be a little rude, but that is more in the eye of the beholder. If it was too personal they might not tell you.

I can't think of any law which (in the US anyway) prohibits you from asking anyone any question (other than solicitation of a crime).

As Craven noted, it might be thought to be rude, but that's another issue.

You indicated you had already asked her; what response did you get ?

They are pulling your leg! A sugar glider as a service animal?

Commonly Asked Questions About Service Animals in Places of Business (http://www.ada.gov/qasrvc.htm)
Service Animals have to be dogs.

National Service Animal Registry (http://www.nsarco.com/service-definitions.html)
Scroll down to Emotional Support Animals. They are not limited to dogs.

Too many people take advantage of this. Notice how this site directs you to a site that will get you a letter to need an ESA. Like getting a script for online medical drugs.

"Service Animals have to be dogs."

And a man's spouse has to be a woman. Sure.