The long-running legal battle over Georgia’s illegal immigration law could continue for months and keep a hotly debated part of the statute on hold if the state decides to appeal the case to the U.S. Supreme Court.

Georgia officials said Tuesday that they were still considering their options after the 11th U.S. Circuit Court of Appeals in Atlanta rejected their request for a rehearing in the case.

The state had asked the appeals court to reconsider its decision against a part of the law that would punish people who knowingly transport or harbor illegal immigrants while committing other crimes. In August, the court ruled the measure is pre-empted by federal law, which already prohibits such activities.

Another part of the statute — nicknamed the “show-me-your-papers law” — has been on hold while the case was before the appeals court. That other provision would give police the option to investigate the immigration status of suspects they believe have committed state or federal crimes and who cannot provide identification or other information that could help police identify them.

Georgia has about 90 days to appeal to the U.S. Supreme Court, which could accept or decline such a case. Under that scenario, the state’s show-me-your-papers law could remain on hold until the Supreme Court acts.

“We are considering our options and no decisions have been made at this time,” the Georgia Attorney General’s Office said in a statement issued Tuesday.

Omar Jadwat, the senior staff counsel for the American Civil Liberties Union’s Immigrants’ Rights Project, said such an appeal would face long odds considering the Supreme Court’s decision in June to strike down three parts of Arizona’s immigration law.

The court invalidated sections of Arizona’s law that would permit police to make warrantless arrests when people commit deportable offenses, punish people who fail to carry official immigration papers and punish illegal immigrants who apply for work in Arizona. That decision, Jadwat said, bolsters legal arguments against the Georgia law that would punish people who knowingly transport or harbor illegal immigrants in the state.

“They would be swimming against a very swift current in the other direction,” said Jadwat, who is part of a coalition of civil and immigrant rights advocates that sued to block parts of Georgia’s immigration law. “And a lot of that current comes from the Supreme Court’s own recent decision in the Arizona case.”

If Georgia decides against appealing to the Supreme Court, the show-me-your-papers law — also known as Section 8 of House Bill 87 — could go into effect next month at the soonest under court rules, said attorneys following the case.

Meanwhile, local police — who have put their preparations to enforce that law on hold amid the court battles — indicated Tuesday that they would remain in a holding pattern. For example, Lt. Col. Ron Hunton, the field operations commander for the Cherokee County Sheriff’s Office, said in an email that his agency “will await some definitive ruling/direction from the court.”

Carlos Campos, a spokesman for the Atlanta Police Department, said: “Absent any further action to stay enforcement of Section 8 of HB 87, the Atlanta Police Department shall implement a comprehensive training plan and will begin enforcing the new law.”