Yes, you can use the EIN because those numbers are usually the same. You can also just call the employer to request/verify the number. I think it will generate an error if you leave it blank.
It is also sometimes known as a tax ID number or taxpayer ID. Because the EIN, or tax ID, is used for federal tax purposes, it stays the same from state to state. Some states require a separate state tax ID, however, to pay state-specific taxes
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