The Interest and Dividends Tax Instructions, page 3, Line 2 states:
Enter on Line 2 any taxable annuities or the actual cash or property distributions you received or constructively received from "S" corporations, partnerships or LLCs, trusts or estates with transferable shares. These distributions are subject to tax in New Hampshire as a “dividend”. (Transferable means that you can freely transfer your shares without causing a dissolution of the organization or without prior approval of the other members.) Taxable annuities are those annuities not invested in a tax deferred investment plan pursuant to RSA 77:4-b.
77:4-b Interest and Dividend Income of Employee Benefit Plans and Tax Deferred Investments Not Taxable. – Notwithstanding any provisions of RSA 77:4 to the contrary, interest and dividend income received by an employee benefit plan as defined by the Employee Retirement Income Security Act of 1974, section 3, or any successor act enacted for the purpose of regulating employee benefit plans, or an individual retirement arrangement, Keogh plan or any other arrangement pursuant to which payment of federal tax on the income thereof and of the plan sponsors, participants and beneficiaries is deferred, shall at no time be considered taxable income under RSA 77:4, either to the plan or arrangement or to its sponsors, participants or beneficiaries, irrespective of when or whether all or any portion of such income is accumulated or expended for the benefit of, or distributed in any form or manner to, such sponsors, participants or beneficiaries.
If your annuity qualifies as non-taxable under these rules, it would not be entered on line 2.