Officials say they're investigating Hodgkinson's whereabouts, associates, web postings and "potential motivations."
Authorities are searching his home in Illinois.
The FBI says five people overall were taken to hospitals with gunshot wounds, including the shooter, Scalise, a Capitol Police officer, a congressional staffer and a lobbyist. Another congressman suffered minor injuries. Hodgkinson later died.
Meanwhile, the Capitol Police says one of its officers is in good condition after having been shot in the ankle and another was treated and released with a minor injury.
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