As an initial matter, you need to determine if your Ukraine-based employee is a U.S. citizen or not.
If your employee is a U.S. citizen (or a U.S. resident alien), then he is subject to the same taxation and withholding requirements as if he was working inside the United States. (more on that) In order to avoid additional taxation on his earned income in the Ukraine, a U.S. citizen may be able to use foreign earned income exclusions to avoid double taxation. (see )
On the other hand, if your employee is not a U.S. citizen (or a U.S. resident alien), then he is considered a nonresident employee and is generally not subject to the reporting and withholding requirements for U.S. income tax purposes. It does not matter that payment is received from a U.S. bank because, for tax purposes, the nonresident employee makes the income where he performs the job–in this case the Ukraine. However, you may have some payroll tax liability in Ukraine. To determine what liability you may have in the Ukraine, you really need to obtain professional advice.
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