NEW YORK (AP) — A judge said Tuesday he’s optimistic that a pretrial hearing will end this week in Luigi Mangione’s New York murder case in the killing of UnitedHealthcare CEO Brian Thompson.

“Hopefully we wind up on Thursday,” Judge Gregory Carro said at the hearing, which is in its third week of testimony.

Mangione, 27, is seeking to exclude items seized during his Dec. 9, 2024, arrest in Altoona, Pennsylvania, including a gun and notebook that prosecutors say tie him to Thompson’s shooting five days earlier in Manhattan.

Prosecutors have called more than a dozen witnesses so far, with at least one more expected after an off-day on Wednesday.

On Tuesday, a Pennsylvania police evidence custodian, a New York City police homicide commander, and an investigative analyst from the Manhattan district attorney’s office testified.

Mangione has pleaded not guilty to state and federal murder charges. The pretrial hearing applies only to the state case. His lawyers are making a similar push to exclude the evidence from his federal case, where prosecutors are seeking the death penalty.

Mangione was arrested after customers spotted him eating breakfast at a McDonald’s in Altoona, a Pennsylvania city about 230 miles west of Manhattan. The restaurant’s manager told a 911 dispatcher customers suspected he was the shooter.

Mangione’s lawyers argue that anything found in his backpack should be excluded from his trial since police didn’t have a search warrant and lacked grounds justifying a warrantless search. However, prosecutors claim the search was legal given the context and safety checks during an arrest. Items found included a 9 mm handgun matching the one used in Thompson’s murder and a notebook allegedly detailing threats against health executives.

As testimony continues, the implications of this pretrial hearing could greatly affect Mangione's future, with both state and federal charges pending against him.