The Austin American-Statesman, for its Wednesday editions, reported the suit alleges the electronic system violates state law because it does not produce paper ballots, so voters have no way of knowing whether their picks are properly recorded.
Appeals lawyer Kristofer Monson, representing Secretary of State Hope Andrade, says voters cannot show they have been harmed and the lawsuit should be dismissed.
Attorney Timothy Herman, for the National Association for the Advancement of Colored People, says a paper record is necessary to protect voting rights.
The high court did not immediately rule Tuesday.