Every certificate described in section 42 of this chapter, and the proof or acknowledgment of the certificate, shall be recorded at full length, and a reference shall be made to the liber and page, or other unique identifying number, containing the certificate, in the minutes of the discharge of the mortgage made by the register upon the mortgage. If the register of deeds is authorized by the board of commissioners to reproduce deeds, mortgages, maps, instruments, or writings, as provided in section 2 of 1964 PA 105, MCL 691.1102, and the mortgage does not exist in a hard copy medium, it is not necessary for him or her to make reference to the liber and page containing the certificate on the liber and page containing the mortgage. Instead, reference to the liber and page containing the certificate shall be made in the index to the permanent index of mortgages.