The short answer is -- we don't know for sure. Because Mitt Romney is refusing to release his tax returns, we are left to speculate based on what is publicly available, and what is publicly available suggests he very well may be.
Even if Mitt Romney isn't dodging taxes entirely, it's more than likely he is paying a capital gains tax rate of roughly only 15%, far below your typical teacher or police officer.
Additionally, the FBI now appears to be investigating Bain Capital, as a recent FOIA request denial would seem to suggest.
Is the FBI Going After Bain Capital?
The answer to the headline question is yes. About two weeks ago, the FBI evoked FOIA exemption 7(a) and denied access to all Bain Capital records on the grounds that "there is a pending or prospective law enforcement proceeding relevant to these responsive records; and that release of the information contained in these responsive records could reasonably be expected to interfere with the enforcement proceedings."
What this all means is anyone's guess, but it seems perfectly clear now that the more "safe" and "electable" Mitt Romney may have more skeletons in the closet than any of the other candidates.
What we do know for sure is that Mitt Romney's economic record is atrocious, and there's plenty to scrutinize irrespective of what any ongoing investigation turns up.