A statement from the Secret Service obtained by PEOPLE confirms Odom has been charged with one count of attempted murder.
Officials say Odom tossed several items – including some flash drives – onto the White House lawn. None of the items were found to be hazardous, according to the statement.
Remington, 55, was shot six times during Sunday's shooting. He has regained consciousness, according to news reports.
Coeur d'Alene Police Department via The Spokesman-Review via AP
Investigators say Odom was in the Marines between 2000 and 2006, and that the Coeur d'Alene, Idaho, man pre-planned the shooting. Police say he has a history of mental illness, but that he had no criminal history prior to Sunday.
Remington was shot a day after leading the invocation at a campaign event for Republican presidential hopeful Ted Cruz, according to authorities. Detectives do not believe Remington's support of Cruz prompted Sunday's violence.
Odom attended services at the church before allegedly shooting Remington. Police claim he had not prior affiliation with the church before Sunday's incident.
Odom is being held without bail. It is unclear if he has an attorney who could comment on his behalf.