The murder trial of a federal agent charged in a Waikiki McDonald’s shooting death has started jury selection. But there’s still uncertainty about where the case could end up.

Christopher Deedy’s attorneys are appealing to have the case moved to federal court. The 9th U.S. Circuit Court of Appeals will hear oral arguments on it in June.

Deedy is accused of killing a Hawaii man in November 2011 while in town for the Asia-Pacific Economic Cooperation summit.

A U.S. District Court judge in August denied his motion to have the case moved to federal court.

Prosecutors argue the appeal is moot because things are moving forward in state court and because Deedy withdrew a motion to dismiss the case because he was acting as a federal law enforcement officer.