Although you have not said, it seems likely that the police are charging your partner with �Failing to stop/report an accident�.
The status of the car park (private or public) is probably not an issue. Most car parks to which the public have �unfettered access� are public places for the purposes of the various Road Traffic laws, regardless of who owns the land. The only exceptions are places such as private car parks belonging to office blocks where access is restricted only to drivers with specific permission.
Defences against the offence include not being aware that an accident had taken place, ot taking reasonable steps to exchange details with the owner of the property/vehicle with which the collision took place.
This is one of the very few motoring offences for which custody is available (maximum six months) though this option is reserved for serious �hit & run� type offences where serious damage, injury or death occurs. The normal penalty in court for the type of incident you mention is a fine of about one week�s net income (reduced by a third for a guilty plea) and a minimum of five penalty points.