How do treaty tie-breaker rules decide residency when two countries both claim me?

When you qualify as a tax resident of both the U.S. and your home country in the same year, the residency article of the tax treaty between them applies a tie-breaker to assign you to just one. The factors are applied in order: where you have a permanent home, then your center of vital interests (closer personal and economic ties), then your habitual abode, and finally your citizenship; if all else fails the two governments resolve it. "Winning" the tie-breaker for the other country can let you be taxed by the U.S. as a nonresident on a treaty-based position, filed with Form 8833. This is a sophisticated area and the U.S. "saving clause" limits how citizens and green-card holders can use it. Read your specific treaty's residency article carefully, since the wording and ordering differ by country.