UPDATED FOR TAX YEAR 2019
New Hampshire requires a tax return only if you had taxable interest or dividend income of more than $2,400 or $4,800 (if filing jointly).
New Hampshire does not tax an individual's earned income (W-2 wages). The state does tax, at a 5% rate, income from dividends and interest.
If you are below the filing requirements, just ignore TurboTax's suggestion to prepare a NH return.
[Edited | 3/26/2020 | 12:05pm PDT]