Eliminating those two critical pieces of evidence – that point to a murder weapon and motive – would be a big win for Mr Mangione’s legal team.

But the chances of that happening are “virtually non existent”, said Dmitriy Shakhnevich, a criminal defence attorney in New York.

He said that’s because there are a number of exceptions to constitutional rules that law enforcement must obtain a warrant for personal searches, including some that may cover this case.

“In a case like this where there’s a manhunt for a violent suspect who committed this alleged crime in plain view in New York City, nobody’s getting a warrant,” Mr Shakhnevich said.

“When they get him, they’re going to search him.”

Prosecutors say they have other key evidence against the defendant, including DNA or fingerprints on items discarded near the crime scene.

Mr Mangione’s attorneys are probably aware of the long odds of getting evidence excluded, Mr Shakhnevich said.

He added that the main reason why defence lawyers hold these type of proceedings is to preview trial testimony from law enforcement.

So far, the court has heard from New York Police Department Deputy Commissioner of Public Information Sgt Chris McLaughlin, who was asked to review surveillance images from after the shooting.

Prosecutors in court also played CCTV showing the killing. A worker who handled security cameras at the McDonald’s in Altoona testified as well.

Mr Shakhnevich said the legal team wants to have this type of information from witnesses so they can be aware of what people might say at trial, and to be on the lookout for any inconsistencies in their statements.

“The benefit of the hearing is that you get to have law enforcement officials testify, and you get to bind them to testimony for a trial later on,” he said.

Mr Mangione’s legal team has also been pushing to bar the federal government from seeking the death penalty.

They have said comments from high-ranking officials, including Attorney General Pam Bondi, accusing Mr Mangione of the murder have prejudiced his case, which they claim is motivated by politics.