Alabama officials on Tuesday asked the Supreme Court to consider a state abortion law that could serve as the basis for overturning the landmark Roe v. Wade ruling, which legalized the procedure nationwide in 1973.

The case concerns the Alabama Unborn Child Protection from Dismemberment Act, a 2016 law that banned a late-term abortion procedure that critics call “dismemberment abortion.”

Dilation and evacuation, as it is known clinically, involves breaking apart the fetus while he or she is still alive and vacuuming out the remains. Abortion defenders argue the grim procedure is necessary in rare cases between the 15th and 18th week of pregnancy and that there is no viable alternative.

Citing Supreme Court precedent, the Atlanta-based 11th U.S. Circuit Court of Appeals upheld a federal judge’s ruling striking down the statute. Two of the three judges on the appellate panel that considered the case expressed their belief that the high court in 1973 wrongly decided the Roe v. Wade case. They invited the current Supreme Court to consider taking the Alabama case.

On Tuesday, the office of Alabama Attorney General Steve Marshall (pictured above right) made it official and filed notice asking the high court to take the case. The state cited similar laws pending in federal appeals courts in New Orleans and St. Louis.

“Dilation and evacuation, as it is known clinically, involves breaking apart the fetus while still alive and vacuuming out the remains.”

“The constitutionality of a state ban on dismemberment abortion is an important question of national significance,” state lawyers wrote. “Litigation over similar abortion laws is pending in several other courts.”

The Supreme Court grants less than 1 percent of the petitions it receives, so it is far from certain that the Alabama appeal even will be heard. It takes four justices for the Supreme Court to take a case.

Abortion opponents have expressed hope that new Justice Brett Kavanaugh will lead the high court to strike down Roe. He replaced Justice Anthony Kennedy, who was the deciding vote in a 5-4 decision to uphold Roe in a 1992 case.

Related: Here’s the Abortion Case That Could Overturn Roe v. Wade

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Even if the court agreed to hear the case, the outcome is far from certain. Justice Clarence Thomas is the only current member of the court who has voted to strike down the abortion precedent. The other conservative-leaning justices — including Kavanaugh — have not ruled squarely on Roe.

Some scholars have expressed skepticism that the court would take on Roe v. Wade so soon after Kavanaugh’s arrival. Chief Justice John Roberts has a reputation for incrementalism and a concern about the court’s perceived legitimacy.

Finally, if the court took the Alabama case, justices could opt for a narrow ruling that allows prohibitions against a specific type of abortion without addressing the broader issue of abortion’s overall legality.