TurboTax should handle the situations in which the distribution might not be taxable at the state level. Box 16 is just reporting how much the distribution was, not what is taxable at the state level.
So do as Annette said and enter the Box 1 amount in Box 16. If you enter your state of residence in your personal information, then if your state doesn't tax or all of the distribution (like military pension, etc.), then TurboTax will see the state in your personal information and in the pages after the initial entry of the 1099-R data, you will be asked about the source of the distribution so that TurboTax can properly report the taxable amount on the state return.
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