Most of the sounds a Maytag refrigerator makes are normal operating sounds. In particular, the buzzing sound your Maytag refrigerator makes may occur when the ice maker water valve hookup fills with water. Since the refrigerator is typically installed on or against hard surfaces such as walls, floors and cabinets and may have foam insulation --- an energy-efficient but not sound-absorbent insulation --- these surfaces, combined with the less sound-absorbent insulation, may make the sound seem louder.
If the Maytag refrigerator has an ice maker, but the refrigerator is not yet connected to the water supply, you may also hear a buzzing sound. The buzzing sound comes from the water valve and may be audible as the system attempts to fill the valve with water.
If you hear the buzzing sound coming from your Maytag refrigerator when the refrigerator is correctly hooked up to a water line, it is normal and there is no need to do anything. Check the water line connection and make sure it is installed correctly, if necessary. If you have not yet connected the refrigerator to the water supply, turn off the ice maker until you do. Turning off the ice maker typically involves raising the wire shut-off arm.
While Maytag claims this sound is generally normal or fixed quickly by turning off the ice maker, you may wish to get a second opinion if the sound is excessively loud or does not stop even after you've turned off the ice maker. Contact Maytag directly for further assistance --- have your model and serial number ready for quicker assistance --- or consult with a qualified appliance repair person.