Police should investigate claims an "out of control" tram crossed a road "at speed [and] at right angles to the traffic", a railway society has said.
Passengers claimed the Snaefell Mountain Railway tram crossed the A18 at about 15:30 BST on 4 August.
The railway was temporarily shut for a health and safety investigation, though the Manx Electric Railway Society (MERS) said police should investigate.
The Isle of Man Constabulary said they would not be part of the investigation.
The tram travelled about 180ft (54m) before switching from a modern braking system to a Victorian one in order to stop. No-one was hurt.
Passenger Nick Douglas said it was a "frightening experience" with the driver "wrestling to gain control".
The railway has a speed limit of 12mph, but the Health and Safety at Work Inspectorate (HSWI) ordered it to remain closed until its operators could "ensure compliance with an 8mph limit".
A government spokesman said the railway was "operating again after trials... confirmed the effectiveness of speed monitoring equipment and management procedures".
A MERS spokesman said it was a "serious road traffic incident on a public road [which] should be properly investigated".
"This tram crossed the A18 Mountain Road at speed, at right angles to the traffic.
"This was a dangerous incident in which the lives of the travelling public were threatened and people were put in terror."
The Isle of Man government said the investigation "was being handled under the appropriate legislation - the Health and Safety at Work Act - by the proper authority, the HSWI".
An HSWI spokesman said there would be no further comment until its investigation was completed.
The railway, built in 1895, is located on the east coast of the Isle of Man and runs between the village of Laxey to the summit of Snaefell, the island's only mountain.
In 2016, an electric tram was destroyed after derailing and crashing in the same area, though no-one was on board at the time.