There's been a lot of questions as of late, and quite a few reports about Android Auto and Apple CarPlay keeping data from your smartphone once it's unplugged from the car. Here we are talking about the car and not the Android Auto app on your smartphone. While Google and Apple do collect a little bit of information from your car, it's not everything that your car could give to them. There were reports last year that Google wanted a full OBD-II dump, which was untrue. Now when it comes to data from your smartphone, you still shouldn't be worried.
Neither Google's Android Auto or Apple's CarPlay collects data from your smartphone. The only data that it collects is the ID of the phone (think MAC address) which is of no use to anyone that may get into your car and doesn't have your smartphone. So this means that neither service is collecting data from your phone, at least data that you should be worried about. With many of us having all sorts of social networks, banking accounts, emails and much more on our smartphone. It is a good thing to think about, but there's nothing here to be worried about. According to employees at Google, Apple, and many car makers, this is the case. If you're really that worried about it, we'd recommend deleting the profile before letting someone borrow your car - or if you are using a rental car, before returning the car.
In fact, you are actually more likely to leave data from your smartphone onto your car when using Bluetooth alone. Where as Android Auto and Apple CarPlay are merely projection services. Typically Bluetooth will ask for permission to your phonebook, which will then be downloaded and give your car easy access to your numbers so that you can make calls in the car. Remember that data is kept in the car until you erase it. For most people, that's not an issue either, but that's still more data than what Android Auto leaves behind.
So if you're looking to get Android Auto fairly soon, perhaps in your next car. Don't be worried about the data that might be collected or even left in the car. You're likely to be more at risk when using a public WiFi Hotspot without a VPN.