When the U.S. Supreme Court decided this month that the presidency isn’t a shield against a New York prosecutor’s criminal investigation, the justices didn’t say whether the same goes for civil suits against the president in state courts.

That has quickly become a question in two closely watched defamation lawsuits filed by women who say President Donald Trump smeared them while denying their sexual assault allegations.

Lawyers for the women, E. Jean Carroll and Summer Zervos, are now trying to persuade New York courts that the U.S. Supreme Court’s ruling  strengthens their arguments for letting the suits go forward. Trump’s attorneys are contending just the opposite.

The dispute comes with one of the cases now before New York’s highest court, which is weighing whether a sitting president is constitutionally protected from being sued in state courts.

“The answer is no” under the U.S. Supreme Court’s reasoning, Zervos attorneys Beth Wilkinson and Moira Penza wrote in a letter Friday to the top-level state Court of Appeals.