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“We really did not have the authority or meet the criteria to issue an Amber Alert, but we did so anyway because of the circumstances,” she said.

Police found Mr. Tatum’s 2007 Chevrolet Blazer parked at a Red Roof Inn in Oxon Hill. Mr. Tatum checked into the hotel the night before. When investigators went to search his room, they made a gruesome discovery: Mr. Tatum’s wife, Andrea Tatum, was inside dead from what appeared to be a gunshot wound to the head.

A person who knew the couple later told police that Mrs. Tatum wanted to leave her husband. The same person said Mr. Tatum expressed interest in buying a handgun.

After discovering Mrs. Tatum’s body, police obtained a warrant for the couple’s Southeast D.C. home. Inside the home, officers found $87, cellphones, children’s clothing and shoes, as well as a photo of Relisha, according to a copy of a search warrant for the home.

D.C. Council member Jim Graham, the Ward 1 Democrat who oversees the Committee on Human Services, plans to hold a hearing Friday to discuss safety procedures at the homeless shelter.

In the meantime, police said, the search for Relisha will continue.

“We have not given up hope that we may still find Relisha alive,” Chief Lanier said.