Upon completion of the quest Accidents Happen, you will see Gromm sitting around Olav's Tap and Tack. If you kill Gromm (one shot or not), his body won't just drop dead. Gromm will mysteriously disappear. No one will witness his murder and you will gain no bounty. (Only tested once successfully on the Xbox 360 and during the quest A Matter of Honor while Alval Uvani is present in the inn). Tested successfully and after completion of the Dark Brotherhood.
After the quest Accidents Happen, when gromm goes to Olav's Tap and Tack he will attack everyone in the inn.(Xbox 360)