I believe its currently regulated by NHDOT like the Cog Railway is.
As I posted 5 years ago (p.10) on the Cog Railway thread this could change if the federal government has there way.
FRA could potentially have jurisdictions over railroads with a bridge length of 10 feet or more and with the covered bridge the White Mountain Central, may be subject to the rule change if it ever comes to pass.
It takes real skill to choke on air, fall up the stairs and trip over nothing. I have those skills.