A car had liquid poured over it at the entrance to Grouville Arsenal on Rue a don after a fight between three men last Friday evening (31 July).
Two men arrived in a Jeep at around 9:30pm, got into a fight with another man who was in the area.
It's understood an accelerant was then poured onto the car which caused structural damage.
It is believed all men know each other.
Since the disturbance, a 33-year-old man has been arrested on suspicion of affray and a 38-year-old man has been arrested on suspicion of affray and grave and criminal assault.
Both have been released on police bail.
Several cars passed the area at the time - and police want the drivers of those cars, along with anyone else with information, to contact them on 612612. Crimestoppers can also be contacted on 0800 555 111 and via an online form.

Haut du Mont trial: Island Energy 'placed health and safety at risk'
Deportation recommended after sex-demanding attacker jailed
Teenage boy arrested on suspicion of sexual touching at Millbrook Park
Eyes up! It's Air Display day...
Haut Du Mont Trial: 'It could explode', jury hears 999 calls
Haut Du Mont Trial: Worker checking gas valves spent almost 'entire' time on his phone
Red Arrows still expected for Jersey Air Show
Haut Du Mont Trial: Gas works were 'sloppy, unsafe, and cut corners', allege prosecutors