Air carrier flight crew reported parking brake failure at gate.

Narrative

I was the First Officer on Flight XXXX. It was nighttime and we were parking at gate in ZZZ as normal. The Captain called for the parking checklist and we ran it. After completion of the checklist I stowed my checklist and began putting my headset away. When I glanced up I saw a signal from the marshaller with his hands crossed over his head and as I saw this I could tell in my peripheral vision the aircraft was moving back. I reached for the brake pedals and announced to the captain 'parking brake; did you set the parking brake'. As we began to slow the Captain engaged the parking brake and the aircraft came to a stop. The Captain opened the window to verify everyone outside was okay and everyone said they were okay and then verified everyone inside was okay and it appeared everyone was okay. After that we were towed back into the gate; deplaned without issue and I found nothing abnormal during the post flight walk around. Captain said she set the brake so either the brake had gotten dislodged from the set position/detent or it had not been set. As a First Officer; I could double check to verify the parking light is on after running the parking check and then before doing anything else look to the marshaller for the signal that the airplane is chocked.