Look at the instructions for NJ-1040
you will prorate your NJ basis in your Traditional IRA ( which requires you have the detailed records of all IRA contributions while a NJ resident).
There is nothing equivalent to prorate or otherwise account for a basis in a 401k distribution.
That's why TurboTax doesn't do it.
If NJ does deduct the 401k contribution from wages (which I conceded above), there is no issue with 401k distributions.
