If there is ever a chance that you might use it (or something similar to it in the future), I would most definitely do the paperwork.

If you don't do the paperwork, then that means that they own the code (laws may vary on this, of course), and can use it in their own product or sell it to someone else.

Of course, IANAL, but IP management has become an important topic lately, and this is one of the issues.