Contributions to a standard 401(k) are pre-tax. Meaning any money your employer pays into it, either in lieu of paying you or as a matched contribution, does not get taxed at the time of the contribution. If you ever take money out of your 401(k), then it will be taxed. State and local municipalities can NOT tax your 401(k) contributions if the IRS doesn't.

There are some things to watch out for with this advice, however. There are contribution limits that can't be exceeded or the excess will be taxed. You also need to know if your plan is a Roth 401(k), as these are post-tax plans. The best advice I can give you is to call the administrators of your 401(k) at both your places of employment and find out for sure that your plan is pre-tax or post-tax type.

Most likely your local government official is confused about what they can tax because of the minute differences of a Roth 401(k), contributions vs distributions, or perhaps the wording of what they are asking you to report is vague.