To best answer this question, you must call the building department in the city/village where your Mother is living. Every building department has different laws and requirements as it comes to getting permits.
Simplest answer is every municipality is different. I would contact the building department and give details about the project.
Permitting is almost always required when it comes to plumbing / electrical / roofing / structure / bathrooms / any type of addition or HVAC . They are concerned with contractors doing the work that are properly licensed and carry adequate insurance. PA requires all contractors to be licensed with the state and have workers comp and liability insurance.
Each municipality typically has a license fee and may require additional insurance.
I am from PA and it could be diffrent situation in any county. The easiest way is just you should contact the building department and give details about the project. I hope that helps.