In order to manage your contacts, access to your contacts, including notes, is requested. This app runs exclusively from your iOS device. This app does not upload your contacts to any servers whatsoever.
The app may prompt you to grant it access to your contacts from your iPhone Settings, and if it does, simply turn on "Contacts" as shown below:
If you don't have the option to turn on "Contacts," you may have restrictions turned on. To fix it, go to your iPhone Settings > General > Restrictions, and either completely disable restrictions, or turn off restrictions for "Contacts" only: