How can I find out if a vapor barrier is requried for finishing a basement to code?
I'll answer the second question first:


  Where would I go looking for any such information for my location? 


Your city's building and code inspector's office. 

But note that because something is to code doesn't necessarily mean it has to be done that way--provided you can show why your way is better. Which leads to your first question:


  Does anyone know if the concept of vapor barriers ever come in to the code compliance of finished basements?


It does in many places, but today is highly discouraged from most modern building science perspectives. 

When I finished my last house's basement, it was in a place that required plastic vapor barriers. I did a lot of research and came to the conclusion that it's a terrible idea and was able to convince my code department of that. Details of that can be found in my answer to the question here:

https://diy.stackexchange.com/a/8644/1209

Note the links provided in the comments by  Brad Mace which point to Building Science Corporation's recommendations--which were the same ones I went from.

The executive summary of why vapor barriers are bad in a basement is that a basement will often have moisture problems on EITHER side of the barrier. In both cases, you'd be trapping moisture rather than letting it escape. It's better to allow a certain amount of moisture permeability.