How you handle this issue will depend on the circumstance of the characters and the tone of the delivery. The first option—putting it all in one sentence—renders the delivery calm and collected:

Did you leave it in your car, in your office or at school?

The speaker may have thought through the options ahead of time or know them well enough that they don't come as a surprise. I can imagine the husband of a forgetful woman rattling this off while making a peanut butter and jelly sandwich as she riffles around looking for her lost item.

Breaking it up into separate sentences suggests something different:

Did you leave it in your car? What about your office? Is it at school?

This doesn't sound as premeditated as the first option and it implies more disorder. While the speaker isn't necessarily calm, he has the presence of mind to speak in full sentences. He's paused in the making of his peanut butter and jelly sandwich. It sits, open faced, on the counter while his attention is on his wife.

If you want a more frantic tone, you might abandon full sentences:

Did you leave it in your car? Your office? School?

This smacks of urgency. The sandwich is long forgotten and he's overturning the pillows of the couch with his wife.

Of course, you can always use narrative to create or reinforce tone. But don't rely on narrative alone when dialogue can do the work, too.