Not long, the law says “shall immediately by the quickest means of communication” give notice, we are usually thinking of hours and less. But there is no specific time-period stated in the law.
61-7-108. Immediate notice of accidents. The driver of a vehicle who knows or reasonably should have known that the driver has been involved in an accident resulting in injury to or death of any person, striking the body of a deceased person, or property damage to an apparent extent of $1,000 or more shall immediately by the quickest means of communication give notice of the accident to the local police department if the accident occurs within a municipality, otherwise to the office of the county sheriff or the nearest office of the highway patrol.
If you have been in car accident in which you were not at fault it is always a good idea to call the police. They will write a report and sometimes issue a ticket. But that is also an independent record of the crash.