Internet connection is only used for fetching map data through the Google Maps API, and crash reporting through Google Play.
Any data saved in the app (saved locations and preferences) are only synchronized to your personal Google Drive storage for back-up. You may opt out of this through your device/Google account settings.
Data obtained through the Fused Location API is only used for plotting your location on the Map in the app, and is not shared with any external parties.
Crash reporting through Google Play only collects logs from crashes with no personal data included.