KardiaMobile does not require cellular service. A phone that only has Wi-Fi will work fine.
Connectivity of some sort is required to create an account. Once an account is complete and active, KardiaMobile does not require a Wi-Fi or mobile connection to record EKGs or to save it to the mobile device.
Connectivity is required to sync automatically with the AliveCor server, share your EKG, or print directly from Kardia app. If you do not have a Wi-Fi or mobile connection at the time of the ECG recording, you can print the data later when you have such a connection and the sync will happen automatically at that time.