AURORA, Colo. — On the afternoon of June 2, the authorities say, a former music teacher named Christian Paetsch walked into a Wells Fargo bank waving a gun and ordered everyone to lie down.

About 15 minutes later, a phalanx of police cars descended upon an intersection a few miles away, blockading dozens of shocked motorists — including Mr. Paetsch, whom the authorities had tracked with a GPS device buried in the $26,000 he was accused of stealing.

But with only the faintest physical description and unsure which vehicle the device was in, the police trained their weapons on all 20 cars at the intersection and ordered people to show their hands. For nearly two hours, the police ordered every driver and passenger to step out of their cars, even handcuffing some of them, before discovering the missing money and two loaded firearms in Mr. Paetsch’s S.U.V.

The case, now winding its way through the federal court system, is being watched by Fourth Amendment lawyers and law enforcement experts. While advanced technology now gives the police the power to shadow a suspect moments after a crime is committed, there are still legal questions over how wide a net the authorities can cast while in pursuit.