Yes and no—the Plegium app must be open to maintain the Bluetooth connection to your device and therefore be able to send emergency alerts when you activate it, but the app can run in the background and your phone can be locked. If the app is completely closed, it won’t be able to receive the activation signal from your spray or alarm button.
On iOS, the Plegium app needs permission to run in the background. Enable this by going to Settings → Apps → Plegium → Background App Refresh → On.
On Android, change the following setting: Settings → Apps → Plegium → Battery → set to “No restrictions” / “Unrestricted”.
The spray/alarm button reconnects automatically when the app is opened again, as long as it’s within Bluetooth range of your phone. You can check the connection status in the app at any time.