Yes for an RV Refrigerator to operate properly it needs to be level. The older the model of Fridge; the more important it is that it is kept level. A good rule of thumb is that the fridge can be plus or minus 2 degrees from plum. That equates to half a bubble out of the level line. The newer fridges have a bit more tolerance.
Unlike your home refrigerator an RV Refrigerator relies on gravity to aid it in cooling down. The more out of level it is the less efficient it becomes in keeping food items cold. The video below does a great job of explaining the inner workings of an RV Refrigerator.
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