Many places have restrictions on propane in tunnels. Falling under transporting hazardous materials. Has little to do with whether you "turn it off" or not, I think. (Unlike fuel-stations)
It is more an issue of what the hazardous material might cause, if you happen in an accident in the tunnel and the tanks get damaged.
The Baltimore tunnels (described here: http://www.mdta.maryland.gov/propane.html) also see propane as a hazardous materials transport and state the below.
vehicles carrying bottled propane gas in excess of 10 pounds per container (maximum of 10 containers), bulk gasoline, explosives, significant amounts of radioactive materials, and other hazardous materials are prohibited from using the Fort McHenry Tunnel (I-95) or the Baltimore Harbor Tunnel (I-895). The Francis Scott Key Bridge (I-695, the Baltimore Beltway) is a convenient alternative route for crossing Baltimore's Harbor.
FYI. Notice that with the right RV GPS, many of these concerns go away, although none are to be trusted (always watch for signs, I hear the ticket can be extreme).
I travel with two RV GPSs and have been comparing.
Garmin's RV 760 (new as of June last year) is too dumb to take propane into consideration. Despite multiple hazardous materials routing being in its brother the Dezl 760 (truck GPS).
Rand McNally's RV GPS has a specific propane configuration (tank size and number of tanks).
When testing a route forced to cross the water at Baltimore, the Garmin will consistently tell you to use the tunnels (illegally), while the Rand McNally RV GPS will route through the tunnels only in car mode (no propane consideration) and ALWAYS send you over the bridge when routing in RV mode. (at least with my configuration, with a 38 Gallon propane tank)