Rio de Janeiro subway is fast, clean and reliable but does not connect Sugar Loaf and Corcovado Mountain (where Christ the Redeemer statue is located).
Differently than cities like London, Paris or New York, the regular tourist in Rio de Janeiro takes the subway very few times (if any). The most convenient way to travel from Sugar Loaf to Corcovado Train station is by taxi.
See here photos of both: Sugar Loaf and Christ the Redeemer statue atop Corcovado Mountain