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Please don't shoot the messenger here (hopefully having all the facts will help you "see around some corners") but for Real estate your ESTATE will have to file a gift tax return a IRS form 706NR, and the exemption is 60,000 (this may have been indexed for inflation) .... intangibles sich as stocks and bonds are exempted but for US situs real estate no exemption exists
See this, from IRS here: http://www.irs.gov/Individuals/International-Taxpayers/Some-Nonresidents-with-U.S.-Assets-Must-File-Estate-Tax-Returns
"Executors for nonresidents must file an estate tax return, Form 706NA, United States Estate (and Generation-Skipping) Tax Return, Estate of a nonresident not a citizen of the United States, if the fair market value at death of the decedent's U.S.-situated assets exceeds $60,000."
Deceased nonresidents who were not American citizens are subject to U.S. estate taxation with respect to their U.S.-situated assets.
U.S.-situated assets include American real estate, tangible personal property, and securities of U.S. companies. A nonresident’s stock holdings in American companies are subject to estate taxation even though the nonresident held the certificates abroad or registered the certificates in the name of a nominee.
As to the rest of your assets? No, as a non-resident, your NON US situs property is not an issue and not under US jurisdiction
So my assets in Singapore will not be subjected to US estate tax?
I should say as a non ( US resident AND NonUS citizen) -- If you were a citizen, your total estate may be subject to estate taxes
no US interest OR jurisdiction unless you were a US citizen
By the way here's an EXCELLENT piece on estate and gift taxation for non-residents: http://www.carrmcclellan.com/publications/estate-and-gift-tax-rules-for-nonresident-aliens/
and just so you'll have it in one place, here is the official IRS guidance again: http://www.irs.gov/Individuals/International-Taxpayers/Some-Nonresidents-with-U.S.-Assets-Must-File-Estate-Tax-Returns
I see that you're typing ... I'll wait
is it a better option to have the apartment in Minneapolis registered in an entity like a LLC
That IS a good idea for liability protection (business creditors, lawsuits, etc cannot come after your personal assets for liabilities associated with the LLC) ... but from an estate OR income tax perspective an LLC is a pass-through. The LLC does not pay tax, but rather PASSES THROUGH its income and losses to the owner(s)