The overnight tryst began in Baltimore with three men, two dressed as women.
It continued at a motel on the highway and when one of the men woke up yesterday, his two cross-dressing companions, and his Ford Escape, were gone.
The dark-coloured SUV was headed south on the Baltimore-Washington Parkway. Its driver, in what authorities believe may have been a mistake, took a restricted exit leading to a security post at the campus of the National Security Agency at Fort Meade, Maryland.
An NSA statement said the driver ignored police commands to stop and instead accelerated towards a police vehicle as at least one officer opened fire. The stolen Ford crashed into the cruiser. One man died at the scene, and the other was rushed to hospital. An NSA officer was also injured, though officials did not say how.
What had at first looked like an attempt to breach security at the listening post that eavesdrops on communications throughout the world now appears to be a wrong turn by two men who police believe had robbed their companion of his vehicle and perhaps did not stop because there were drugs inside.
A spokeswoman for the Baltimore FBI said early in the investigation that authorities "do not believe [the incident] is related to terrorism". A law enforcement official said: "This was not a deliberate attempt to breach the security of NSA ... not a planned attack."
Police have not named the people involved. The NSA statement did not say whether either person in the car was struck by gunfire or injured in the crash.
Details about how the incident began were pieced together with information from several law enforcement officials and others.
A Howard County police spokeswoman confirmed that the men involved stayed at a Jessup motel and that the owner of the Ford called police to report it stolen.
One police official said it appeared that the owner of the Ford picked up the other two men in Baltimore, though detectives had not confirmed that account entirely.
The officials do know that the three men checked into the motel and stayed the night. One official familiar with the investigation described the episode as "prostitution and drug-related".