The NY tax may increase when you first put in the 1099-R, but you also need to carefully step thru ALL of the questions that follow the main 1099-R form. There is one (shown below ... but may be a bit different this year) where you need to indicate which pension system the 1099-R came from. After doing that, it should limit the NY taxes...assuming you are a member of one of the eligible NY retirement systems.
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