Residents and citizens of the United States pay income tax on worldwide income.
You need to report the rental income on Form 1040 (Schedule E) . if you do not you will not be in compliance with the law.
According to Article 6 of the Tax Treaty with Ukraine the income from real property may be taxed by the Ukraine as well as the United States. Income tax paid to the Ukraine will be eligible for the foreign tax credit on Form 1116 .