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
Service Animals have to be dogs.

National Service Animal Registry
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.