It turns out that -- for much of the nation's history -- non-citizens
were permitted to vote. It was only during the post-WWI wave of
immigration to the U.S. -- and the resultant anti-immigrant backlash
-- that non-citizen voting rights began to be seriously restricted.
A recent article on the topic from the Atlanta Journal-Constitution
can be found here:
Cities debate whether noncitizens should vote
which notes, in part:
--In 1968, New York City allowed anyone who had a child in its school
system to participate in community school board elections. That went
away when Mayor Michael Bloomberg restructured the school system...
--In 1992, Takoma Park, Md., voters approved giving noncitizens the
ballot...Five other municipalities followed. In Chicago, noncitizens
have voted for a decade in school elections.
--In 2003, the cities of Cambridge and Amherst in Massachusetts
approved the franchise for all residents regardless of nationality.
They await state legislation to enable it.
So, as you can see, the answer to your question is TRUE. There are at
least a handful of jurisdictions in the U.S. where non-citizens can
vote in local elections. Many other jurisdictions have this issue
under active consideration, most notably (these days) San Francisco:
Non-citizen parents may vote in S.F.
I hope this answers your question fully, but feel free to let me know
if you need any additional information or clarification of what's
search strategy: Google search on [ non-citizen us vote ]