Final answer:
While the question seems related to operational procedures in emergency medical services or transport logistics, it does not directly pertain to any academic subject. In physics, distance and displacement are two different concepts: distance is the total path length traveled, and displacement is the straight-line change in position.
Step-by-step explanation:
The statement given in the question, '​Prior to leaving the hospital to return to the station, you must record the trip odometer reading,' is more procedural than conceptual, and it seems to relate to standard operating procedures in a field like emergency medical services (EMS) or transport logistics. Since the context is not fully clear and the question does not pertain directly to any academic subject, providing an answer of true or false is not possible. However, I can address a related concept in physics.
An object's distance traveled is the total length of the path taken between two points, while displacement is a vector quantity that refers to the change in position of the object. It is entirely possible for an object to record a distance traveled of zero while still having a non-zero displacement; this would occur if the object returns to its starting point. Conversely, an object may record a non-zero distance traveled while having a displacement of zero if it moves in a closed loop.
To further illustrate, consider the following example: If you drive a car at exactly 50 mph and then apply the brakes until it stops, the trip odometer will record the distance you traveled while the car slowed to a stop. This is different from displacement, which would be the straight-line distance from where you started applying the brakes to where you stopped.