A county clerk in New York refused Thursday to file a more than $100,000 judgment from Texas against a doctor accused of prescribing abortion pills to a woman near Dallas, setting up a potential challenge to laws designed to shield abortion providers who serve patients in states with abortion bans.

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.