NEW YORK (AP) -- Luigi Mangione's lawyers urging a judge Thursday to throw out his state murder charges in the killing of UnitedHealthcare CEO Brian Thompson, arguing that the New York case and a parallel federal death penalty prosecution amount to double jeopardy.

If that doesn't happen, they want terrorism charges dismissed and prosecutors barred from using evidence collected during Mangione's arrest last December, including a 9 mm handgun, ammunition and a notebook in which authorities say he described his intent to "wack" an insurance executive.

Mangione's lawyers also want to exclude statements he made to police officers who took him into custody at a McDonald's restaurant in Altoona, Pennsylvania, 230 miles (about 370 kilometers) west of New York City, after a five-day search.

Among other things, prosecutors say the Ivy League graduate apologized to officers "for the inconvenience of the day," and expressed concern for a McDonald's employee who alerted them to his whereabouts, saying: "A lot of people will be upset I was arrested."

Thompson's Dec. 4 killing outside a Manhattan hotel "has led to a legal tug-of-war between state and federal prosecutors as they fight for who controls the fate of 26-year-old Luigi Mangione," his lawyers, Karen Friedman Agnifilo, Marc Agnifilo and Jacob Kaplan wrote in a 57-page court filing.

They called the dual state and federal cases, plus a third in Pennsylvania involving gun possession and other charges, "unprecedented prosecutorial one-upmanship." They said prosecutors "are trying to get two bites at the apple to convict Mr. Mangione" of murder.

"Yet, despite the gravest of consequences for Mr. Mangione, law enforcement has methodically and purposefully trampled his constitutional rights," his lawyers wrote. They allege officers questioned him without telling him he had a right to remain silent and searched his property without a warrant.

The Manhattan district attorney's office said it would respond in court papers.

The defense's demands to end or limit Mangione's state case could preview his legal strategy for his federal murder case, where prosecutors intend to seek the death penalty. The state charges carry a maximum punishment of life in prison.

Mangione, who turns 27 on Tuesday, has pleaded not guilty in both cases. He has been held in a Brooklyn federal jail since authorities whisked him to New York by plane and helicopter after his arrest.

Mangione is due back in court for the state case on June 26, when Judge Gregory Carro is expected to rule on the dismissal request. He next federal court date is Dec. 5, a day after the one-year anniversary of Thompson's death. No trial date has been set in either case.

Prosecutors had said they expected the state case go to trial first, but Friedman Agnifilo said last week that she wants the federal case to take precedence because it involves the death penalty.

Along with seeking to dismiss the state case, Mangione's lawyers alternatively asked Carro to throw out charges alleging he killed "in furtherance of terrorism" and as an act of terrorism. They argue there are "absolutely no facts to support this theory" and that charging him under a post-9/11 terrorism statute flouts the intent of lawmakers.

Surveillance video showed a masked gunman shooting Thompson from behind as the executive arrived for UnitedHealthcare's annual investor conference. Police say "delay," "deny" and "depose" were scrawled on the ammunition, mimicking a phrase commonly used to describe how insurers avoid paying claims.

Manhattan District Attorney Alvin Bragg has said that the ambush "was a killing that was intended to evoke terror."

Mangione's federal charges include murder through use of a firearm, which carries the possibility of the death penalty, along with two counts of stalking and a firearms offense.

Last month, U.S. Attorney General Pam Bondi announced that she was directing Manhattan federal prosecutors to seek the death penalty for the killing, calling it "an act of political violence" and a "premeditated, cold-blooded assassination that shocked America."

The killing and ensuing search leading to Mangione's arrest rattled the business community while galvanizing health insurance critics who rallied around Mangione as a stand-in for frustrations over coverage denials and hefty bills.

In their filing Thursday, Mangione's lawyers argued that the conflicting theories of the state and federal cases -- intending to "intimidate or coerce a civilian population vs. stalking a single person" -- has created a "legal quagmire" that makes it "legally and logistically impossible to defend against them simultaneously."

"This situation is so constitutionally fraught that we are hard pressed to find precedent for such an unprecedented situation," Mangione's lawyers wrote.