Many web languages offer developers tool sets with which they can quickly build and deploy stateless applications. However, it is still important to ensure that all connections from the application are being appropriately closed. While it is generally considered good practice to close all open connections, failing to do so in Redis can[1] lead to problems like stale connections or memory leaks.
Many newer Redis drivers will implement connection pooling and close connections for you (behind the scenes) once they go out of scope. It is recommended to thoroughly read through your driver's documentation on connection management, just to be clear on how connections to Redis are handled and closed.