From the IRS it appears that you're exempt from self-employment taxes but not necessarily from income taxes. You should check with HRD.
Green Card Holders (Lawful Permanent Resident)
If you are a green card holder working for a foreign government or international organization, you generally must report your earnings as wages but are not subject to self-employment taxes on those earnings and may not voluntarily pay self-employment tax on those earnings.
If you expect to have income tax due at the end of the year, you must make estimated tax payments because your compensation is not subject to withholding. Estimated payments are made using Form 1040ES, Estimated Tax for Individuals. Forms are due on the following four dates: April 15th, June 15th, September 15th, and January 15th of the following year. There is a penalty for failure to make estimated tax payments on a timely basis.
Answers are correct to the best of my ability but do not constitute legal or tax advice.
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