What to do if my son was in a car accident in a private parking lot and it’s questionable who was at fault?

Your son should contact his insurance company.  Since there wasn't any police report which would have established who was at fault, the insurance company/ companies if the other driver was insured will determine which party was at fault in the accident.  If the other driver was at fault, your son would file a property damage claim  and if applicable a separate personal injury claim with the other driver's insurance.  If your son was at fault, the other driver will file a property damage claim and if applicable a personal injury claim with your son's insurance company.  It is possible that the other driver did not have insurance.  If that is the case and the other driver is at fault, your son could file an uninsured motorist claim with his insurance company provided that he has uninsured motorist coverage.  If the other driver was at fault and did not have insurance and your son did not have uninsured motorist coverage, your son will need to sue the other driver for negligence for his (your son's) property damage (cost of repairs to your son's vehicle) and personal injury if applicable.

If your son was injured in the accident and the other driver was at fault, first be certain that the other driver has insurance or if he doesn't that your son has uninsured motorist coverage before running up huge medical bills.  Once insurance is verified, your son should proceed with his medical treatment.  When he completes his medical treatment and is released by the doctor, your son should obtain his medical bills, medical reports, and documentation of any wage loss.  Compensation for the medical bills is straight reimbursement.  Compensation for wage loss is straight reimbursement.  The medical reports will document the nature and extent of your son's injuries and will be used to determine compensation for pain and suffering.  Compensation for pain and suffering is an amount in addition to the medical bills.  Assuming that either the other driver had insurance or if not, your son has uninsured motorist coverage, if your son is dissatisfied with settlement offers from the insurance company, he can reject the settlement offers and file a lawsuit for negligence against the at-fault driver.  If the case is settled with the insurance company, no lawsuit is filed.  If the case is NOT settled, your son will need to file a lawsuit for negligence against the at-fault driver prior to the expiration of the applicable statute of limitations or your son will lose his rights forever in the matter.