(a) The department shall file each notice of security interest received by the department with the required fee and maintain a record of all notices of security interests filed by the department:

(1) Alphabetically, under the name of the owner;
(2) Under the vehicle identification number;
(3) Under the certificate of title number; and
(4) In the discretion of the department, by any other method it determines.
(b) The department before issuing or reissuing a certificate of title shall check the name of the owner and the certificate of title number of the vehicle against the record provided for in subsection (a).