A county clerk cited the state’s shield law for declining to enforce a $100,000 judgment imposed in Texas against a New York health-care provider, setting up a likely showdown at the Supreme Court.

On Thursday, citing New York’s shield law, the acting clerk of Ulster County in Kingston, N.Y., Taylor Bruck, said he would not grant Texas’ motion seeking to enforce the Collin County order. He also refused to allow Texas to file a summons that sought to force Dr. Carpenter to pay the penalty and comply with the Texas ruling.

A New York county clerk refused to process a $113,000 fine against a New York doctor found guilty of prescribing abortion-inducing medications in Texas.