A flirty non-committal way of answering this is simply, “Guess you’ll have to wait and see”.
“Well, I’d have to say that’s a bit contextual…”
I’d hint at being diverse, while still striking a safe-ISH tone. A modest edge is ok - I’d think…
“I’m clean as a whistle. Want to blow me?”
You’re welcome. 
(missed edit window)
Seriously, how about: “I’m squeaky clean, except where I’m filthy. Details on request.”
This. Plus it opens the door for clarification on her part, or more double entendre. The latter would be more fun. 
While elkin’s approach would also leave no doubt, it strikes me as… a little too serious and/or humorless for a flirty exchange.
How about, ‘Unclean only in mind’?
Guess you’l hav to see if I have festering sores? All set, thanks.
“I’d have to say I’m avoiding the topic by being a weenie.”
This doesn’t seem like a mystery – among women, men in general, and single men especially, have the reputation of being legendary, stupendous slobs. So she brings it up jokingly, perhaps hinting that she’d like to see your apartment. You know… see if its clean <wink>.
From an old Limelighters song intro:
"…remember our motto here at Camp…
‘Clean mind, clean body…take your pick.’"
Tell her you insist on a clean kitchen…
Maybe the whole point was that you were supposed to deny it.
“Are you a clean man?”
“No, I’m a dirty boy.”
Yes indeed and fully clothed at that
“Are you a clean man?”
“Generally very much so. But the right woman could convince me to be bit dirty…”
Nah, scratch that. go with what Cervaise said in post #23.
So, stuyguy, did you ever find out what she meant? How did you reply?
She was just being playful, with no real intent I think. When we finally got together, it never came up at all.
I want to thank everyone for their advice and theories. I especially want to thank Cervaise for the best comeback in the thread (“I’m clean as a whistle. Want to blow me?”). Boy, I wish I had used that line, even if it meant getting my virtual face slapped!