The interest is not going to be exempt. The interest must be paid by the United States in order to be tax exempt and in the case of the Repurchase Agreements, it is not. The seller of the repurchase agreement collects the exempt interest and the buyer is paid the agreed upon price later. While that interest may be set based on the interest of the obligation, it's not paid by the issuer, and is therefore not eligible to be exempt.
Several states have addressed this in rulings or court cases. Though I didn't check all states with income taxes, it is safe to assume they will all view it the same way. The interest being received on a repurchase agreement is considered interest on the loan of the securities, not interest on the treasury obligation. That treasury interest is paid to the
If take a look at SC Revenue Ruling #91-15 you can see a few examples of how courts have ruled on this in a handful of states and the legal underpinning of those decisions.
The discussion on Repurchase Agreements begins near the bottom of page 5.
I didn't check every state with a state income tax, so I suppose it is possible that your state views it differently, but it is not likely.
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