After serious accidents in the later nineteenth century, American and Canadian railways brought in time-service rules. Watches carried by train crews had to be inspected regularly by approved watch inspectors.
The exact standards differed between railways and changed over time. Commonly cited requirements included a large (typically 16 or 18 size) open-face watch, a minimum number of jewels, adjustment to temperature and several positions, lever setting, and a plain, bold dial. Check the specific standard for the railway and period before relying on any one list.
Lever setting means the crown cannot set the hands by accident. Instead, the bezel and crystal are removed and a small lever is pulled out. It is one of the easiest features to spot.
'Railroad' written on a dial does not prove the watch was approved. Many watches were marketed with railroad names. The movement grade, the maker's records and any inspection papers are better evidence.