NEW YORK (AP) -- A high-stakes hearing in the New York murder case against Luigi Mangione continues Thursday, a year to the day after prosecutors say he gunned down UnitedHealthcare CEO Brian Thompson.

Mangione, 27, has pleaded not guilty to both state and federal charges. Before any trials get scheduled, his lawyers are trying to preclude the eventual jurors from hearing about his alleged statements to law enforcement officers and items -- including a gun and a notebook -- allegedly seized from his backpack.

The evidence is key to prosecutors' case. They have said that the 9 mm handgun matches the firearm used in the killing, that writings in the notebook laid out Mangione's disdain for health insurers and ideas about killing a CEO at an investor conference, and that he gave Pennsylvania police the same fake name that the alleged gunman used at a New York hostel days before the shooting.

Thompson, 50, was shot from behind as he walked to an investor conference on Dec. 4, 2024. He became UnitedHealthcare's CEO in 2021 and had worked within parent UnitedHealth Group Inc. for 20 years.

The hearing, which started Monday and could extend to next week, applies only to the state case. But it is giving the public an extensive preview of some testimony, video, 911 audio and other records relevant to both cases.

It's not immediately clear what witnesses or evidence are expected Thursday.

Tuesday's court session displayed police body-camera video of officers confronting Mangione at a McDonald's in Altoona, Pennsylvania, and concluding -- to their amazement -- that he was the much-publicized suspect in Thompson's killing five days earlier.

They interacted with Mangione for roughly 20 minutes before telling him he had the right to remain silent. The officers asked his name, whether he'd been in New York recently and other questions, including: "Why are you nervous?"

Officers tried to play it cool and buy time by intimating that they were simply responding to a loitering complaint and chatting about his steak sandwich. Still, they patted Mangione down and pushed his backpack away from him. About 15 minutes in, they warned him that he was being investigated and would be arrested if he repeated what they'd determined was a fake name.

After he gave his real one, he was read his rights, handcuffed, frisked again and ultimately arrested on a forgery charge related to his fake ID.

The video also provided glimpses of officers searching his backpack, a matter that will likely be explored further as the hearing goes on.

Mangione's lawyers argue that his statements shouldn't be allowed as trial evidence because officers started questioning him before reading his rights. The defense contends the backpack items should be excluded because police didn't get a warrant before searching his bag.

Manhattan prosecutors haven't yet detailed their arguments for allowing the disputed evidence. Federal prosecutors have maintained that police were justified in searching the backpack to ensure there was nothing dangerous inside and that Mangione's statements to officers were voluntary and made before he was under arrest.

Many criminal cases see disputes over evidence and the complicated legal standards governing police searches and interactions with potential suspects.