The only tool needed that is specifically made for refrigerator repair is a condenser brush. A condenser brush is a long, bristled brush made to clean dirt and dust from the condenser grille. Other common tools are likely needed as well.
Other tools that you may need to repair a refrigerator are flat-head and Phillips screwdrivers in a few different sizes. You may also need a hair dryer for melting ice and an extendable inspection mirror to see in difficult places. Electrical pliers, electrical tape, a flashlight and a volt-ohm meter to test circuits are also tools that are needed for refrigerator repair.