This depends on the remodel work. Changing, moving or repairing walls, floors, ceilings etc. requires a Building Permit. This does not cover cosmetic items like new carpet, linoleum, painting, etc. Changing, moving or repairing electrical requires an Electrical Permit. Changing, moving or repairing mechanical requires a Mechanical Permit. Changing, moving or repairing plumbing requires a Plumbing Permit.
Some items require two permits like a Central Air Conditioning. The air conditioner is mechanical requiring a Mechanical Permit and the electrical for the AC requires an Electrical Permit.