When a taxpayer has omitted or neglected to make a return of his property for taxation or has made a false return for or in any year, including business personal returns filed with the Department of Revenue, and the county auditor of the county in which the return should have been made is informed of that fact within the period of time within which the State may bring suit for the collection of the taxes, the auditor shall notify the defaulting taxpayer, or, if he is dead, his personal or legal representative, to appear before him at his office at a time set in the notice and shall assess the property not returned as prescribed in §§ 12-37-760 to 12-37-780. If notice must be given to a nonresident, the notice must be served by publication in some newspaper and by mailing a copy of it to the nonresident as prescribed for service of nonresidents by Title 15, and taxes must be assessed and collected as provided by statute.