As a green card holder, you are a U.S. tax resident. However, the definition of residency under U.S. tax laws does not override tax treaty definitions of residency. If you are a dual-resident taxpayer (a resident of both the United States and another country under each country’s tax laws), you can still claim the benefits under an income tax treaty.
The income tax treaty between the two countries must contain a provision that provides for resolution of conflicting claims of residence (tie-breaker rule). If you would be treated as a resident of the other country under the tie-breaker rule and you claim treaty benefits as a resident of that country, you are treated as a nonresident alien in figuring your U.S. income tax. For purposes other than figuring your tax, you will be treated as a U.S. resident. For example, the rules discussed here do not affect your residency time periods as discussed in FAQ 17 above.
If you are a dual-resident taxpayer and you claim treaty benefits as a resident of the other country, you must file a return by the due date (including extensions) using Form 1040NR or Form 1040NR-EZ, and compute your tax as a nonresident alien. You must also attach a fully completed Form 8833 if you determine your residency under a tax treaty and receive payments or income items totaling more than $100,000. You may also have to attach Form 8938.