Its up to you. but if it was me I would.. The back is glass to and will break to. That's why I would use a case on it,, but its up to you and if you want to keep it looking good
I've had my phone for about 9 months now. Have been using this screenprotector the whole time. Comes with a glass front one, and a plastic back. Works really well. I have never used a case on the phone, and no scratches yet.