Residential parking permit

working on applying for a residential parking permit to have parking by my sublease downtown. My vehicle is currently registered to my parents address which is on the other side of Madison. Based on the city's website it looks like if you are a Madison resident you can only get a permit for the car's registered address (which is my parent's and doesn't help me park downtown). I plan on calling the city tomorrow but wonder if anyone has had success with the same sort of situation.