What is important is of there is an amount in box 14 on the 1099-R. This shows the amount of state tax withheld. If there was no state tax withheld, then you might as well blank out boxes 15 and 16. In fact, in same cases, TurboTax will become quite confused if you have something in 15 or 16 but nothing in 14, so it's really better in this case to leave all three boxes blank.
On the other hand, if there is an amount in box 14, then you have to enter something in boxes 15 and 16. In most cases for a 1099-R distribution, the box 16 amount is the same as the box 1 amount, and this can be used if you are unable to contact the 1099-R issuer.
Whether or not you need to file the state return is quite a different animal and depends on other factors. You need to look at the requirements for each state to see if you are required to file a return. Generally, you owe taxes in the state you live in and to the state(s) you work in, but there are many exceptions
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