Winterizing Question

I have a 2nd home in West Virginia mountains used on weekends. It gets quite cold there and when we leave, I turn off the water and open the faucets (hot and cold) in the basement to drain the water lines in case power goes out so the pipes don't burst. I leave the heat set at 50 degrees. I have a Rinnai RL75i tankless water heater. Should I do anything to the water heater if I'm draining the pipes? So far I've just left it on and done nothing to it, but it just dawned on me that this may not be a good idea.

Thanks!

With no water in it there is no flow to trigger an ignition cycle, but it does chew up some standby power to no good end just idling there. Killing the power to it doesn't hurt, and precludes any bizarre condition that would make it dry-fire (like a lighting-hit scrambling the control logic in an optimally bad way, which is by definition rarer than being hit by lightning. :-) )

FWIW: Whenever I leave my place for more than a few days I kill the power to the tankless unless there sub-20F temperatures forecast (since my tankless is also my space-heating boiler.)