Bill is this case is the same as invoice or statement. The person overpaid. The government agency is acknowleging the overpayment. It could also be a credit notice, or an invoice with a credit balance.

I think it is a somewhat unusual UK or Commonwealth type use. At least I didn't find much on google, but here's another example from India.

However, he mentioned that the
Respondent did not provide copy of the bill inspite of his request on the ground that it was a
credit bill. He was only verbally advised of the credit and no copy of the bill was given.

http://www.mercindia.org.in/pdf/Omb_Ord_63_of_2008_dt_15_10_...

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Note added at 32 mins (2010-04-10 20:28:01 GMT)
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Here's one more where they used "credit bill" to mean credit balance. Further into this website, they indicate they will not issue a refund, but will apply the credit against the customer's future charges.

"ECG is proud to announce a new way to save money on your telecommunication services. It's simple. Refer a customer to ECG and you'll receive a credit bill. Just how much can you save? It's up to you. Your credit is based on your referral's long distance usage.
You'll receive 5% of that usage credited to your account.
The more people you refer the more you save! And these aren't one-time savings either! You will continue to receive a credit every month for as long as your referral remains an ECG customer! Now that's something to talk about!"

http://www.telephoneroad.com/index.html




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Note added at 34 mins (2010-04-10 20:29:45 GMT)
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Yes it can also be called a credit note.