In most cases, asking your scene partner a question "corners" him or her. It violates the usual magic trick of improv, which is to create potential to go in many directions, thereby making life easy for your partner. If only one direction is "correct", then your scene partner will have to see it or be perceived as "wrong".
Also, questions tend to be weak offers compared to equivalent statements.
A question that Adds Information sometimes opens up lots of exciting possibilities, though.
Compare:
"In what year did the Monkees break up?"
with:
"The Monkees broke up years ago. And we're going down the same path, brother."
Which makes life easier for your scene-partner?
Compare:
A. "Is that a rake?"
B. "Yes."
A. "I think it's autumn. What do you think?"
B. "Yeah, I think it's autumn, too."
A. "Do you think we should pick up these leaves?"
B. "Yeah, sure."
with:
A. "There's my rake."
B. "Hubert stole it! I knew it!"
A. "He 'just wanted to do a little gardening'. Well, I say we do a little gardening right now."
B. "Yeah, Hubert's marigolds will never see the light of day again!"
"Have you forgotten everything that Swami Ravasinanja taught us?"
"Oh no, what happened to my lucky checkers?"
"So, um, why so many spare tires?"
If you must ask a question, ask one that opens up many possibilities for an answer.
Compare:
"Are you Dr. Bamburg?"
with:
"So what sort of medicine do you practice, Dr. Bamburg?"