The code-G Form 1099-R reports the portion rolled over from the traditional account in the old plan to the traditional account in the new plan. Answer No when asked if this was rolled over to any kind of Roth account. The code-BG Form 1099-R is for the portion rolled over from the designated Roth account in the old plan to the designated Roth account in the new plan (not to a Roth IRA).
I'm not sure why TurboTax asks the NY-related questions. It seems like None of the above is the only answer that makes any sense as SharonD007 indicates. A 401(k) is a deferred compensation plan.
