If your retirement money is a pension, I don't believe it would be considered interest or dividend. Social Security is not taxed. 401K or IRA distributions are not taxed.
NH has a 5% tax on interest and dividends exceeding $2,400 annually ($4800 for a couple).. Obviously interest and dividends still 'inside' things like 401Ks and IRAs are not taxed.
I would assume many people in retirement may have savings/stocks outside an IRA or 401K and certainly for a modest/large pool of money in that category - interest and dividends would be taxed. Of course with artificially low interest rates these days, it is harder to hit the threshold where taxed.
Not a tax adviser , nor in retirement - if anything here is wrong, I offer a full refund of the amount paid for this advice