Radio case needs to have a proper earth to the body. The outer part of the aerial plug that goes into the case will also provide that but the aerial is often badly earthed to the wing or it's mounting point or not at all. Any "static" or whine that changes with engine speed is related to the generator or any motors, fan, wipers etc., that are running. Normal suppression add-ons usually cure that. AM noise harder to cure than FM. FM not normally much of a problem though.
Poor or unsuppressed plug leads can give problems. Spray some water on the leads and run the engine in pitch black darkness. There shouldn't be any "sparks" but there could be a firework display.