Refer to FIBIS Fact File #4: “Research sources for Indian Railways, 1845-1947” - available from the Fibis shop. This Fact File contains invaluable advice on 'Researching ancestors in the UK records of Indian Railways' with particular reference to the India Office Records (IOR) held at the British Library
An on-line search of the IOR records relating to this railway  gives the following: -
- L/F/8/20/1704 “Madras and Southern Mahratta Railway Company Limited, Contract as to transfer of Mysore-Nanjangud, Birur-Shimoga and Mysore-Bangalore sections of the Mysore Railway to the Mysore Durbar; 1924"
- “British Library Archives and Manuscripts Catalogue” - Search; Retrieved 26 Jan 2016