This can be confusing.
Box 11 has nothing to do with US Gvt interest. Box 11 is for state bonds whose interest is not taxable by the federal government. (And is usually not taxed by the state that issued the bond.)
Most funds will provide a supplementary statement showing the percentage of box 1 (ordinary dividends) that come from US Government obligations (e.g. t-notes, t-bonds). If you do the math and tell TT the amount, then TT will do the right thing so that your state will not tax that US Government dividends/interest.
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