Inheritances and life insurance proceeds are not considered income by the IRS, and therefore, the IRS does not tax beneficiaries when they receive inheritance money. Instead, the IRS taxes the estate of the decedent -- the person who passed away and left the money to you -- before you receive the money. You do not need to pay taxes on your inheritance money, nor should you claim it anywhere on your federal income tax return.
However, if you save the money you received from either source in an interest-bearing account, you will need to claim the actual interest as income on your federal income tax return each year you receive it, even if you never "cash out" the interest and simply leave it in your interest-bearing account. The same holds true if you invest your inheritance and you earn a return, even if you immediately deposit the dividends into an account or re-invest them.
Some states do tax beneficiaries' inheritance money upon receipt; New Jersey does not. New Jersey taxes the estate the same way as the IRS. Therefore, you do not need to report your inheritance money on your state income tax return, either. However, the same rules for investments and interest earned that apply to federal income tax returns, also apply to state income tax returns in New Jersey.
In a nutshell, you do not need to report your inheritance on any federal or New Jersey state tax forms right now. If you later save or invest your inheritance money, you will need to report the interest you earn and/or the dividends you receive on your income tax returns.