what is the VAT refund procedure in USA?

Answer 1

Are we to understand that you are US-based and you have purchased something from the European Union? If so, then there are two possibilities:

Firstly, if you had been able to demonstrate your non-EU status the purchase should have been charged without VAT.

If you were charged VAT then you must apply to the Customs & Excise authority in the country of purchase for a refund. Unless it was a very large purchase it probably won't be worth it.

Answer 2

Since there is no VAT in the US, there are no refunds of VAT.