Both passed breath analysis tests to check for alcohol, according to the police report. When the plane landed, the report said, Mr. Cheney turned to waiting officers and gave a “two thumbs up” sign through the cockpit window.

Officials at the National Transportation Safety Board said they gave a preliminary listen to the plane’s cockpit voice recorder on Friday afternoon, but that may not provide any answers. The recorder, which runs continuously throughout a flight, has only 30 minutes of sound at any one time, and records over itself. The officials said they would interview the pilots over the weekend and would have something to say as early as Monday.

Federal aviation officials said that the last radio communication with the plane was at 6:46 p.m., Central time, and communication did not resume until 8:14 p.m., a gap of 88 minutes, a long time for a commercial jet over the continental United States that has not had a system failure or whose radio is not tuned to the wrong frequency

Image The cockpit voice and flight data recorders from Northwest Airlines Flight 188. Credit... Jonathan Ernst/Getty Images

Pilots normally wear headsets with microphones, or they transfer controllers’ audio to a loudspeaker. Unless the radio was tuned to the incorrect frequency, “if you’re awake, you’re going to hear,” said the former chief executive of a major airline, who spoke on condition of anonymity.

More than a dozen controllers, including those at three radar rooms tracking the flight  one in Denver and two in the Minneapolis-St. Paul area  tried to contact the pilots, said Doug Church, a spokesman for the National Air Traffic Controllers Association. “It was all hands on deck,” Mr. Church said. One Minneapolis-area room made 13 attempts at contact, an official said. The plane was cruising at 37,000 feet about 400 miles west of Minneapolis when the crew stopped responding to air traffic controllers and airline dispatchers an hour and five minutes before its scheduled arrival time of 8:01 p.m., local time.

When the plane should have been descending, it was still flying at a constant altitude, according to FlightAware, a company that provides real-time tracking of airplanes based on radar data from the Federal Aviation Administration. It showed that the plane flew northeast at constant altitude from 7:13 p.m. to 7:53 p.m., Central time, making one 19-degree turn in that period.