I incurred capital losses as a resident alien in the USA. Now, having left the USA, I am a non-resident alien and I am given to understand that I do not have to show capital gains or losses on the tax return form. Does this mean I cannot deduct any of the said losses from future capital gains from now on?
Capital Gains arising from not effectively connected income (Schedule NEC) of 1040-NR, i.e. Stock, Bond, Savings Account, are exempt from US Capital Gains Tax. So if you had Capital Loss carryover, there is nothing to offset with.
"Capital gains of aliens present in the United States 183 days or more if such gains and losses were effectively connected with the conduct of a trade or business within the United States"
For Effectively Connected Income (ECI) and if you are present but not deemed as resident, according to 26 U.S. Code §871. (a)(2),
such gains and losses shall be determined without regard to section 1202 and such losses shall be determined without the benefits of the capital loss carryover provided in section 1212.
Either way, NEC or ECI, your past Capital Loss is useless.