A federal appeals court panel is weighing the constitutionality of a new Mississippi law that requires doctors at abortion clinics to have privileges at local hospitals.

A three-judge panel of the 5th Circuit U.S. Court of Appeals gave no indication how they would rule after they heard arguments in the case Monday, but did raise the possibility that the law posed what they called an “undue burden” on women in the state, the Jackson Clarion-Leger reported.

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The newspaper quoted one member of the panel, Judge E. Grady Jolly, as telling attorney Paul Barnes of the Mississippi Attorney General’s Office that “you’ve got a steep hill to climb when you say the only clinic in the state is closing.”

Barnes replied that the Supreme Court has held that the Constitution guarantees the right to an abortion, but not an unsafe one. He said the new law is designed to ensure the health and safety of Mississippi women.

The state’s sole abortion clinic is urging the panel to strike down the law.  A lawyer for the Jackson Women’s Health Organization said the law would effectively force the clinic to close because its doctors have been unable to obtain local hospital admitting privileges.

In March, a different 5th Circuit panel upheld a similar Texas law that requires admitting privileges. Texas has more than one abortion clinic.