This article only applies to the Android version of Zello.

To use Zello while your device's screen turned off, you will first need to connect an external PTT or wired headset button via Bluetooth. For detailed instructions on how to do so, please reference this support article.

Next, open the talk screen for the contact you wish to chat with. Then, you will be able to continue sending messages using your external PTT device while your device's screen is turned off.

There is no way to switch between contacts while your device's screen is turned off, so you will only be able to send messages to one contact at a time.