If you possess a parking permit for the residents' parking zone, then yes, according to the German Road Traffic Act (StVO), car sharing users holding a resident parking permit can park within your resident's area without charge for an indefinite period, without the risk of receiving a parking ticket.
For additional details, you can inquire at your local council office. If you intend to apply for a parking permit and require confirmation of your status as a car sharing customer, kindly get in touch with your local office.