Questions born of ignorance: Would you even be required to respond to such an individual (off-duty, civilian clothing, child in tow)?
What would be the most likely outcome if you just gave him/her the "What? Are you stupid?" look and walked away?
I know that it would most probably vary from state to state, but just what authority, if any, does such an off-duty LEO have in the absence of criminal activity or even RAS?
I would also have to see more identification than just a badge flashed at me. There are too many realistic-looking fake badges out there for me to rely on just that. (remind me to tell y'all of the time I flashed a badge at an Army CID agent)