WASHINGTON—An investigation targeting President Trump’s top emergency-management official has been referred to federal prosecutors to determine whether criminal charges should be pursued, according to people familiar with the probe.

Brock Long, the administrator of the Federal Emergency Management Agency, and two other federal employees may have broken as many as six laws as they commuted frequently between Washington and Mr. Long’s home in Hickory, N.C., at taxpayers’ expense, said one of the people briefed on the investigation.

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