The request was filed late Tuesday in U.S. District Court on behalf of the family of Tamara "Strawberry" Greene, the Detroit Free Press reported.
The request for a default judgment alternatively asks a federal judge to approve a comprehensive search of the city's computer servers and backup equipment to find deleted e-mails and other data, the newspaper said.
Norman Yatooma, a lawyer for the Greene family, says the recovered data could prove Kilpatrick and the city conspired to block an investigation into Greene's drive-by shooting death in April 2003, several months after she was linked to a rumored party at the mayor's mansion in fall 2002.
Greene's family filed a lawsuit five years ago alleging a Detroit police investigation into Greene's death was quashed by authorities.
City attorneys have two weeks to respond to Yatooma's requests.
U.S. Magistrate Judge R. Steven Whalen then will decide whether to issue sanctions against the city for destroying the computers.
Whalen has said he is "troubled" that the computer was thrown away.
"From city e-mails, to police careers, to memories of deceased loved ones, (Kilpatrick and the city) have destroyed everything in their paths," Yatooma wrote in his request for a judgment.
"Like the underlying investigation into Tamara Greene's murder, the defendants simply terminated or obstructed whatever investigation they did not like," Yatooms wrote.