My father passed away in 2005 and bequeathed his annuity to me and my sister. The funds (approximately $16,000 each) were distributed in 2006 and his estate paid the Federal and Colorado State taxes on it before my sister and I received our share. Because I deposited the entire amount into the bank, my bank reported the amount to the IRS. I need to know if I have to pay additional taxes (Federal and Hawaii State) on this. I'm thinking I may not have to, but I don't want to NOT pay it and then get in trouble for it later.

It depends on the structure of the annuity.

It is likely the annuity was funded with after-tax money. In that case, the initial money used to buy the annuity is tax-free. However, the money that was earned within the annuity grew on a tax-deferred basis, which means it is subject to income taxes when it is withdrawn.

Go get professional tax help on this. The tax pro will need to review the anuuity itself to determine what is taxable and what is tax-free.

I'm sorry, I didn't mention that the 1009 is not under my name, it's made out to my father's estate. All of the paperwork was sent to the executor when he took care of the taxes and settling all of my father's affairs. I only received a copy of the 1099, but since my name is not on it, I was wondering how I would claim it. Does this make a difference on whether or not I need to include the amount in my income tax?

You do NOT claim it. The estateneeds to file a fiduciary return (Form 1041) to pay the taxes on the annuity distribution.