The operator of every motor vehicle which is in any manner involved in an accident within this state, in which any person is killed or injured or in which damage to the property of any one person, including himself or herself, in excess of two hundred fifty dollars ($250) is sustained, shall within 30 days after the accident report the matter in writing to the director. The report, the form of which shall be prescribed by the director, shall contain only the information necessary to enable the director to determine whether the requirements for the deposit of security under Section 32-7-6 are inapplicable by reason of the existence of insurance or other exceptions specified in this chapter. The director may rely upon the accuracy of the information unless and until there is reason to believe that the information is erroneous. If the operator is physically incapable of making the report, the owner of the motor vehicle involved in the accident shall, within 10 days after learning of the accident, make the report. The operator or the owner shall furnish additional relevant information as the director shall require.