Luigi Mangione's defense team wants at least two counts against him in the New York state indictment thrown out.
His attorneys filed a motion that includes photos of Mangione's arrest at a Pennsylvania McDonald's.
Attorney Karen Agnifilo alleges evidence was illegally obtained, that terrorism charges don't apply, and the concurrent state and federal prosecution violate the double jeopardy clause.
Her filing argues his statements to law enforcement were unconstitutional because he wasn't given his Miranda rights, and that any evidence from his backpack should be suppressed because it was obtained without a search warrant.
Agnifilo called it a "legal tug-of-war between state and federal prosecutors" and an "unprecedented prosecutorial one-upmanship."
As an alternative, Agnifilo wrote the court could temporarily halt the state case while Mangione's federal death penalty case plays out.
Mangione is charged in the murder of UnitedHealthcare CEO Brian Thompson. The 26-year-old is accused of ambushing Thompson outside a Midtown hotel in December.
So far, New York state prosecutors have not filed a response.
Mangione faces 11 state charges, including murder and terrorism, in New York, as well as forgery and weapons charges in Pennsylvania. Federal prosecutors have also charged with stalking, a firearm offense, and murder through the use of a firearm. Federal prosecutors say they intend to seek the death penalty.
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Alice Gainer