One of Washington’s leading good-government organizations formally asked the Pentagon to investigate financial conflicts of interest in the Defense Department’s best-known research branch.

The Project on Government Oversight (POGO) asked for the inquiry after news reports that Darpa handed out $1.75 million in contracts to a company owned in part by agency director Regina Dugan and her relatives. What’s more, Dugan is owed $250,000 by her family firm, RedXDefense. POGO wants to verify that Dugan had nothing to do with the contracts, and to determine if “any Darpa employee” dealing with the com...