I don't think so. I think you have to have paid or received a refund from the IRS itself, not a state.

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Only your state had your bank information.

However according to the IRS:

The IRS does not have my direct deposit information. What can I do?

In the coming weeks, Treasury plans to develop a web-based portal for individuals to provide their banking information to the IRS online, so that individuals can receive payments immediately as opposed to checks in the mail.