It depends.
If you are a resident of Washington state, there are no state income taxes and therefore, you would not be required to pay any taxes on the income.
However, depending upon the type of unclaimed funds distributed to you, you may have to report any earnings received from the unclaimed funds on your federal income tax return.
For example, if the unclaimed funds were from a savings account, you might need to report interest income. If the money was from stocks and you subsequently sold those stocks, you would have to report capital gains.
Please see do I need to report a cash inheritance for additional information.
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