It depends on which inverter you have. If you have the type with an automatic transfer switch that changes from drawing power from your battery to using shore power, then you really don't need to do anything, but if you're going to be in one location for an extended time, you can (maybe should) turn off the inverter to preserve it. (sort of like turning off the TV when going to bed). On the other hand, if you have the inverter WITHOUT an automatic transfer switch, then you need to switch from battery power to shore power.
I think "most" new residential refrigerator installations do have the automatic transfer switch so when you plug into shore power, the system automatically selects shore power and puts your batteries on "standby/charge" until you unplug the shore power cord.... Pretty much a seamless operation...
Here is one thread that discusses the options open to you:
http://www.keystoneforums.com/forums...l+refrigerator