Damage to four headstones at Cootamundra Cemetery on Sunday could well have been accidental, rather than a malicious act, according to police.
Officer in charge of Cootamundra police, Inspector Frank Brown, said a car parked near the headstones may have rolled backwards when its driver took his or her foot off the brake, with the handbrake off and the transmission in neutral.
"That's what we're surmising," he said, "there's no other evidence to suggest that someone's been there deliberately carrying on.
"The person who did it may have been a family member of someone commemorated in that section of the cemetery, and is probably quite embarrassed and will not want to come forward."
Those commemorated by the headstones were Michael Phillip Yates (1945-2017), Robert Charles Wilson (1943-2017), Julie Anne Edwards (1966-2017) and Irene Pearl Sullivan (1948-2017).