My tax refund was accidently sent to a closed checking account. The bank captured the funds and kept the amount that was in the negative. Can a Bank do this with federal funds?

The Bank is not a Credit Union either which from what I have heard makes a difference

I am not aware of differences in banks and credit unions with reference to right of offset.

That being said, there may be a question concerning using social security deposits to offset, but I do not believe this question would be applicable to income tax refunds.

In my opinion the bank was within in rights to offset the deposit. Banking relationships are important, so keep talking to your bank and make sure they understand how you are going to honor your debts.

Recap:
You had a checking account that was in the negative. So you had a debt to the bank.

You had money go to that account. In your return you verified probably twice that was where it was to go.

The bank accepted the deposit, per your instructions and with any deposit first paid the overdraft. Excess funds are available to you.

Yes, the bank was absolutely within its rights. The only exception I could see was if you had that overdraft balance listed in a bankruptcy that was discharged. In that event the bank would be prohibited from taking payment.