What to know about abortion lawsuits in US courts this week

When the U.S. Supreme Court undid the nationwide right to abortion last year, it did not remove the issue from the courts.

Instead, it opened a new frontier of litigation, with states passing their own restrictions and opponents challenging them in courts across the country.

This week, at least four state supreme courts are dealing with abortion cases, including a Texas ruling Monday that rejected a woman's individual request for access to an abortion because of pregnancy complications.

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Some things to know about the cases:

Texas woman ends quest for abortion in-state

Most of the lawsuits that have been filed against bans and restrictions are seeking to secure general access to abortion.

But last week, a Texas woman experiencing serious pregnancy complications decided not to wait for those challenges to be resolved. Saying that her condition poses a risk to her health and future fertility, she asked a court for permission to obtain an abortion immediately.

A state district judge issued an order on Thursday allowing Kate Cox to receive an abortion. The state attorney general filed an appeal, arguing that Cox’s situation does not meet the criteria for an exception. He also warned that anyone providing the abortion could still face legal consequences. On Friday, the state’s Supreme Court put the lower-court ruling on hold.

On Monday, before the top court had issued a final ruling, her lawyers announced that she had gone to another state for an abortion. Later in the day, the Texas Supreme Court ruled against her.

RELATED: Texas Supreme Court pauses lower court’s order allowing pregnant woman to have an abortion

Texas doctors had told the 31-year-old Cox that their hands were tied — despite the Texas law's exception for when a woman's life is at risk — and that she would have to wait for the fetus to die or carry the pregnancy to term.

A pregnant woman in Kentucky is also seeking immediate access to an abortion, but the claim she filed Friday does not cite exceptions to that state's law; rather it argues that the ban on abortion at all stages of pregnancy violates the state constitution.

Arizona's dueling laws

Before Arizona was a state, it had a ban on abortion that was overridden by the U.S. Supreme Court's landmark 1973 Roe v. Wade decision, which established a nationwide right to abortion. Just before Roe was undone last year, lawmakers passed a separate ban on abortion after 15 weeks of pregnancy.

There's been confusion and litigation over which law applies. Currently, abortions are available during the first 15 weeks of pregnancy, based on a court ruling last year that said doctors can't be prosecuted for providing abortions during this time frame.

The Arizona Supreme Court is scheduled to hear arguments Tuesday on whether the pre-statehood ban of 1864 — which would prohibit abortions at any stage of pregnancy — should apply.

Meanwhile, Arizona abortion rights supporters are pushing to get a ballot question before voters next year that would undo both bans. Advocates in other states are attempting to put similar questions on the ballot following the success of such a measure in Ohio last month.

Battle between local and state laws in New Mexico

New Mexico is one of seven states that allows abortions to be obtained at all stages of pregnancy, and it's become a major destination for people from states with bans, especially neighboring Texas.

That hasn't stopped some conservative city and county governments in the blue state from passing local abortion bans.

The state's Democratic attorney general is challenging those bans, saying they violate the state constitution's provision prohibiting discrimination based on sex and pregnancy status.

Most of the local laws have been put on hold by the New Mexico Supreme Court while it considers the issue. The court will hear arguments on the challenge on Wednesday.

Legal wrangling in Wyoming

Two hearings before courts in Wyoming this week could shape litigation on the legality of abortion.

In July, Teton County District Court Judge Melissa Owens paused enforcement of a ban on abortion at all stages of pregnancy while she weighs whether to hold a trial on a challenge to the ban.

Owens is holding a hearing Thursday to choose between a trial or making a decision more quickly based on legal arguments put before her.

Prior to that, the state Supreme Court — whose five members were all appointed by Republican governors — will hear arguments Tuesday on whether to let two lawmakers and Right to Life of Wyoming intervene in the case. They contend that Republican state Attorney General Bridget Hill should defend the ban with evidence, not just legal arguments.

Hill said in a court filing that while she doesn't object to parties being added, the case should be decided solely on the legal arguments.

The state has just one clinic that provides abortions with both medication and surgery. The Casper clinic opened in April, after a nearly yearlong delay because of damage from an arson attack. A second, in Jackson, which provides only medication abortion, has said it is closing this week because of high rent and other costs.

Changing laws in Michigan

On Monday, Democratic Michigan Gov. Gretchen Whitmer signed the last piece of a legislative package known as the Reproductive Health Act. The package aims to reinforce and safeguard abortion rights in Michigan after voters last year approved a ballot initiative enshrining the right in the state’s constitution.

The bill repeals a law that had banned insurance coverage for abortion without purchase of a separate rider. The law, coined "rape insurance" by opponents, was passed exactly 10 years ago by a state Legislature that was controlled by Republicans.

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Mulvihill reported from Cherry Hill, New Jersey. Associated Press reporter Joey Cappelletti in Lansing, Michigan, contributed to this report.